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Volumn 2013, Issue , 2013, Pages

Identification of unknown parameters and orders via cuckoo search oriented statistically by differential evolution for noncommensurate fractional-order chaotic systems

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EID: 84893785069     PISSN: 10853375     EISSN: 16870409     Source Type: Journal    
DOI: 10.1155/2013/382834     Document Type: Article
Times cited : (10)

References (92)
  • 1
    • 84865636059 scopus 로고    scopus 로고
    • A semi-analytical method for the computation of the Lyapunov exponents of fractional-order systems
    • 10.1016/j.cnsns.2012.06.013 MR2974358 ZBL1253.35199
    • Caponetto R., Fazzino S., A semi-analytical method for the computation of the Lyapunov exponents of fractional-order systems. Communications in Nonlinear Science and Numerical Simulation 2013 18 1 22 27 10.1016/j.cnsns.2012.06.013 MR2974358 ZBL1253.35199
    • (2013) Communications in Nonlinear Science and Numerical Simulation , vol.18 , Issue.1 , pp. 22-27
    • Caponetto, R.1    Fazzino, S.2
  • 2
    • 34347330038 scopus 로고    scopus 로고
    • A necessary condition for double scroll attractor existence in fractional-order systems
    • 2-s2.0-34347330038 10.1016/j.physleta.2007.05.081
    • Tavazoei M. S., Haeri M., A necessary condition for double scroll attractor existence in fractional-order systems. Physics Letters A 2007 367 1-2 102 113 2-s2.0-34347330038 10.1016/j.physleta.2007.05.081
    • (2007) Physics Letters A , vol.367 , Issue.1-2 , pp. 102-113
    • Tavazoei, M.S.1    Haeri, M.2
  • 3
    • 0041384356 scopus 로고    scopus 로고
    • Chaotic dynamics of the fractional lorenz system
    • 034101 10.1103/PhysRevLett.91.034101
    • Grigorenko I., Grigorenko E., Chaotic dynamics of the fractional lorenz system. Physical Review Letters 2003 91 42 034101 10.1103/PhysRevLett.91.034101
    • (2003) Physical Review Letters , vol.91 , Issue.42
    • Grigorenko, I.1    Grigorenko, E.2
  • 4
    • 84860168517 scopus 로고    scopus 로고
    • Synchronization of fractional order chaotic systems using active control method
    • 2-s2.0-84860168517 10.1016/j.chaos.2012.02.004
    • Agrawal S. K., Srivastava M., Das S., Synchronization of fractional order chaotic systems using active control method. Chaos, Solitons & Fractals 2012 45 6 737 752 2-s2.0-84860168517 10.1016/j.chaos.2012.02.004
    • (2012) Chaos, Solitons & Fractals , vol.45 , Issue.6 , pp. 737-752
    • Agrawal, S.K.1    Srivastava, M.2    Das, S.3
  • 5
    • 77952741594 scopus 로고    scopus 로고
    • Chaos in fractional conjugate Lorenz system and its scaling attractors
    • MR2652675 ZBL1222.37037 2-s2.0-77952741594 10.1016/j.cnsns.2010.02.005
    • Yang Q., Zeng C., Chaos in fractional conjugate Lorenz system and its scaling attractors. Communications in Nonlinear Science and Numerical Simulation 2010 15 12 4041 4051 MR2652675 ZBL1222.37037 2-s2.0-77952741594 10.1016/j.cnsns.2010.02.005
    • (2010) Communications in Nonlinear Science and Numerical Simulation , vol.15 , Issue.12 , pp. 4041-4051
    • Yang, Q.1    Zeng, C.2
  • 6
    • 0036650479 scopus 로고    scopus 로고
    • A predictor-corrector approach for the numerical solution of fractional differential equations
    • DOI 10.1023/A:1016592219341, Fractional Order Calculus and Its Applications
    • Diethelm K., Ford N. J., Freed A. D., A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dynamics 2002 29 1-4 3 22 MR1926466 ZBL1009.65049 2-s2.0-0036650479 10.1023/A: 1016592219341 (Pubitemid 34945390)
    • (2002) Nonlinear Dynamics , vol.29 , Issue.1-4 , pp. 3-22
    • Diethelm, K.1    Ford, N.J.2    Freed, A.D.3
  • 7
    • 84855202563 scopus 로고    scopus 로고
    • Parameter identification of commensurate fractional-order chaotic system via differential evolution
    • 2-s2.0-84855202563 10.1016/j.physleta.2011.12.008
    • Tang Y., Zhang X., Hua C., Li L., Yang Y., Parameter identification of commensurate fractional-order chaotic system via differential evolution. Physics Letters A 2012 376 4 457 464 2-s2.0-84855202563 10.1016/j.physleta.2011.12.008
    • (2012) Physics Letters A , vol.376 , Issue.4 , pp. 457-464
    • Tang, Y.1    Zhang, X.2    Hua, C.3    Li, L.4    Yang, Y.5
  • 8
    • 67649861441 scopus 로고    scopus 로고
    • Dynamic analysis of a fractional-order Lorenz chaotic system
    • MR2554825 ZBL1198.37063 2-s2.0-67649861441 10.1016/j.chaos.2009.03.016
    • Yu Y., Li H.-X., Wang S., Yu J., Dynamic analysis of a fractional-order Lorenz chaotic system. Chaos, Solitons & Fractals 2009 42 2 1181 1189 MR2554825 ZBL1198.37063 2-s2.0-67649861441 10.1016/j.chaos.2009.03.016
    • (2009) Chaos, Solitons & Fractals , vol.42 , Issue.2 , pp. 1181-1189
    • Yu, Y.1    Li, H.-X.2    Wang, S.3    Yu, J.4
  • 9
    • 79961020785 scopus 로고    scopus 로고
    • Parameter identification and synchronization of fractional-order chaotic systems
    • MR2826009 ZBL1245.93039 2-s2.0-79961020785 10.1016/j.cnsns.2011.04.005
    • Yuan L.-G., Yang Q.-G., Parameter identification and synchronization of fractional-order chaotic systems. Communications in Nonlinear Science and Numerical Simulation 2012 17 1 305 316 MR2826009 ZBL1245.93039 2-s2.0-79961020785 10.1016/j.cnsns.2011.04.005
    • (2012) Communications in Nonlinear Science and Numerical Simulation , vol.17 , Issue.1 , pp. 305-316
    • Yuan, L.-G.1    Yang, Q.-G.2
  • 11
    • 1842832060 scopus 로고    scopus 로고
    • Chaos in Chen's system with a fractional order
    • MR2060878 ZBL1060.37026 2-s2.0-1842832060 10.1016/j.chaos.2004.02.013
    • Li C., Peng G., Chaos in Chen's system with a fractional order. Chaos, Solitons & Fractals 2004 22 2 443 450 MR2060878 ZBL1060.37026 2-s2.0-1842832060 10.1016/j.chaos.2004.02.013
    • (2004) Chaos, Solitons & Fractals , vol.22 , Issue.2 , pp. 443-450
    • Li, C.1    Peng, G.2
  • 12
    • 3342927052 scopus 로고    scopus 로고
    • Chaos and hyperchaos in the fractional-order Rössler equations
    • MR2092674 2-s2.0-3342927052 10.1016/j.physa.2004.04.113
    • Li C., Chen G., Chaos and hyperchaos in the fractional-order Rössler equations. Physica A 2004 341 1-4 55 61 MR2092674 2-s2.0-3342927052 10.1016/j.physa.2004.04.113
    • (2004) Physica A , vol.341 , Issue.1-4 , pp. 55-61
    • Li, C.1    Chen, G.2
  • 14
    • 72649090282 scopus 로고    scopus 로고
    • Chaos synchronization for a class of nonlinear oscillators with fractional order
    • MR2577800 ZBL1187.34066 2-s2.0-72649090282 10.1016/j.na.2009.10.033
    • Song L., Yang J., Xu S., Chaos synchronization for a class of nonlinear oscillators with fractional order. Nonlinear Analysis: Theory, Methods and Applications 2010 72 5 2326 2336 MR2577800 ZBL1187.34066 2-s2.0-72649090282 10.1016/j.na.2009.10.033
    • (2010) Nonlinear Analysis: Theory, Methods and Applications , vol.72 , Issue.5 , pp. 2326-2336
    • Song, L.1    Yang, J.2    Xu, S.3
  • 15
    • 70350521756 scopus 로고    scopus 로고
    • Adaptive synchronization of the fractional-order unified chaotic system
    • MR2590911 ZBL1212.37058 2-s2.0-70350521756
    • Zhang R.-X., Yang Y., Yang S.-P., Adaptive synchronization of the fractional-order unified chaotic system. Acta Physica Sinica 2009 58 9 6039 6044 MR2590911 ZBL1212.37058 2-s2.0-70350521756
    • (2009) Acta Physica Sinica , vol.58 , Issue.9 , pp. 6039-6044
    • Zhang, R.-X.1    Yang, Y.2    Yang, S.-P.3
  • 16
    • 18844427587 scopus 로고    scopus 로고
    • Chaos synchronization of the fractional Lu system
    • DOI 10.1016/j.physa.2005.01.021, PII S0378437105000555
    • Deng W. H., Li C. P., Chaos synchronization of the fractional Lü system. Physica A 2005 353 1-4 61 72 2-s2.0-18844427587 10.1016/j.physa.2005.01. 021 (Pubitemid 40684290)
    • (2005) Physica A: Statistical Mechanics and its Applications , vol.353 , Issue.1-4 , pp. 61-72
    • Deng, W.H.1    Li, C.P.2
  • 17
    • 67249140258 scopus 로고    scopus 로고
    • A fractional-order hyperchaotic system and its synchronization
    • 2-s2.0-67249140258 10.1016/j.chaos.2008.04.034
    • Deng H., Li T., Wang Q., Li H., A fractional-order hyperchaotic system and its synchronization. Chaos, Solitons & Fractals 2009 41 2 962 969 2-s2.0-67249140258 10.1016/j.chaos.2008.04.034
    • (2009) Chaos, Solitons & Fractals , vol.41 , Issue.2 , pp. 962-969
    • Deng, H.1    Li, T.2    Wang, Q.3    Li, H.4
  • 18
    • 27744554781 scopus 로고    scopus 로고
    • Chaos synchronization of the Chua system with a fractional order
    • DOI 10.1016/j.physa.2005.06.078, PII S0378437105007132
    • Li C. P., Deng W. H., Xu D., Chaos synchronization of the Chua system with a fractional order. Physica A 2006 360 2 171 185 MR2186261 2-s2.0-27744554781 10.1016/j.physa.2005.06.078 (Pubitemid 41627568)
    • (2006) Physica A: Statistical Mechanics and its Applications , vol.360 , Issue.2 , pp. 171-185
    • Li, C.P.1    Deng, W.H.2    Xu, D.3
  • 19
    • 34548617848 scopus 로고    scopus 로고
    • Generating multi-directional multi-scroll chaotic attractors via a fractional differential hysteresis system
    • 2-s2.0-34548617848 10.1016/j.physleta.2007.04.112
    • Deng W., Lü J., Generating multi-directional multi-scroll chaotic attractors via a fractional differential hysteresis system. Physics Letters A 2007 369 5-6 438 443 2-s2.0-34548617848 10.1016/j.physleta.2007.04.112
    • (2007) Physics Letters A , vol.369 , Issue.5-6 , pp. 438-443
    • Deng, W.1    Lü, J.2
  • 20
    • 77951575404 scopus 로고    scopus 로고
    • Synchronization of chaotic fractional-order systems via linear control
    • MR2656696 ZBL1183.34095 2-s2.0-77951575404 10.1142/S0218127410025429
    • Odibat Z. M., Corson N., Aziz-Alaoui M. A., Bertelle C., Synchronization of chaotic fractional-order systems via linear control. International Journal of Bifurcation and Chaos 2010 20 1 81 97 MR2656696 ZBL1183.34095 2-s2.0-77951575404 10.1142/S0218127410025429
    • (2010) International Journal of Bifurcation and Chaos , vol.20 , Issue.1 , pp. 81-97
    • Odibat, Z.M.1    Corson, N.2    Aziz-Alaoui, M.A.3    Bertelle, C.4
  • 21
    • 80054903851 scopus 로고    scopus 로고
    • A note on phase synchronization in coupled chaotic fractional order systems
    • MR2846880 ZBL1238.34121 2-s2.0-80054903851 10.1016/j.nonrwa.2011.08.016
    • Odibat Z., A note on phase synchronization in coupled chaotic fractional order systems. Nonlinear Analysis: Real World Applications 2012 13 2 779 789 MR2846880 ZBL1238.34121 2-s2.0-80054903851 10.1016/j.nonrwa.2011.08.016
    • (2012) Nonlinear Analysis: Real World Applications , vol.13 , Issue.2 , pp. 779-789
    • Odibat, Z.1
  • 22
    • 84861733446 scopus 로고    scopus 로고
    • Generalized synchronization of the fractional-order chaos in weighted complex dynamical networks with nonidentical nodes
    • MR2929901 ZBL1258.34130 2-s2.0-83655192760 10.1007/s11071-011-0295-9
    • Wu X., Lai D., Lu H., Generalized synchronization of the fractional-order chaos in weighted complex dynamical networks with nonidentical nodes. Nonlinear Dynamics 2012 69 1-2 667 683 MR2929901 ZBL1258.34130 2-s2.0-83655192760 10.1007/s11071-011-0295-9
    • (2012) Nonlinear Dynamics , vol.69 , Issue.1-2 , pp. 667-683
    • Wu, X.1    Lai, D.2    Lu, H.3
  • 23
    • 77955018368 scopus 로고    scopus 로고
    • Bifurcations of fractional-order diffusionless lorenz system
    • 2-s2.0-77955018368
    • Sun K., Sprott J. C., Bifurcations of fractional-order diffusionless lorenz system. Electronic Journal of Theoretical Physics 2009 6 22 123 134 2-s2.0-77955018368
    • (2009) Electronic Journal of Theoretical Physics , vol.6 , Issue.22 , pp. 123-134
    • Sun, K.1    Sprott, J.C.2
  • 24
    • 70449574688 scopus 로고    scopus 로고
    • Chaos in the fractional-order Lorenz system
    • 10.1080/00207160701864426 MR2537927 ZBL1169.65115
    • Wu X.-J., Shen S.-L., Chaos in the fractional-order Lorenz system. International Journal of Computer Mathematics 2009 86 7 1274 1282 10.1080/00207160701864426 MR2537927 ZBL1169.65115
    • (2009) International Journal of Computer Mathematics , vol.86 , Issue.7 , pp. 1274-1282
    • Wu, X.-J.1    Shen, S.-L.2
  • 25
    • 84861729690 scopus 로고    scopus 로고
    • Analytical and numerical methods for the stability analysis of linear fractional delay differential equations
    • 10.1016/j.cam.2012.03.010 MR2926260 ZBL1250.65099
    • Kaslik E., Sivasundaram S., Analytical and numerical methods for the stability analysis of linear fractional delay differential equations. Journal of Computational and Applied Mathematics 2012 236 16 4027 4041 10.1016/j.cam.2012.03.010 MR2926260 ZBL1250.65099
    • (2012) Journal of Computational and Applied Mathematics , vol.236 , Issue.16 , pp. 4027-4041
    • Kaslik, E.1    Sivasundaram, S.2
  • 26
    • 76049124927 scopus 로고    scopus 로고
    • Fractional ordered Liu system with time-delay
    • MR2592631 ZBL1222.34005 2-s2.0-76049124927 10.1016/j.cnsns.2009.08.015
    • Bhalekar S., Daftardar-Gejji V., Fractional ordered Liu system with time-delay. Communications in Nonlinear Science and Numerical Simulation 2010 15 8 2178 2191 MR2592631 ZBL1222.34005 2-s2.0-76049124927 10.1016/j.cnsns.2009.08. 015
    • (2010) Communications in Nonlinear Science and Numerical Simulation , vol.15 , Issue.8 , pp. 2178-2191
    • Bhalekar, S.1    Daftardar-Gejji, V.2
  • 27
    • 23144435914 scopus 로고    scopus 로고
    • A note on the fractional-order Chen system
    • DOI 10.1016/j.chaos.2005.04.037, PII S0960077905003590
    • Lu J. G., Chen G., A note on the fractional-order Chen system. Chaos, Solitons & Fractals 2006 27 3 685 688 2-s2.0-23144435914 10.1016/j.chaos.2005.04.037 (Pubitemid 41084201)
    • (2006) Chaos, Solitons and Fractals , vol.27 , Issue.3 , pp. 685-688
    • Lu, J.G.1    Chen, G.2
  • 28
    • 2442563860 scopus 로고    scopus 로고
    • Identification of fractional chaotic system parameters
    • 2-s2.0-2442563860 10.1016/j.chaos.2004.03.007
    • Al-Assaf Y., El-Khazali R., Ahmad W., Identification of fractional chaotic system parameters. Chaos, Solitons & Fractals 2004 22 4 897 905 2-s2.0-2442563860 10.1016/j.chaos.2004.03.007
    • (2004) Chaos, Solitons & Fractals , vol.22 , Issue.4 , pp. 897-905
    • Al-Assaf, Y.1    El-Khazali, R.2    Ahmad, W.3
  • 29
    • 84861893481 scopus 로고    scopus 로고
    • A new Jacobi operational matrix: An application for solving fractional differential equations
    • 10.1016/j.apm.2011.12.031 MR2930392 ZBL1252.34019
    • Doha E. H., Bhrawy A. H., Ezz-Eldien S. S., A new Jacobi operational matrix: an application for solving fractional differential equations. Applied Mathematical Modelling 2012 36 10 4931 4943 10.1016/j.apm.2011.12.031 MR2930392 ZBL1252.34019
    • (2012) Applied Mathematical Modelling , vol.36 , Issue.10 , pp. 4931-4943
    • Doha, E.H.1    Bhrawy, A.H.2    Ezz-Eldien, S.S.3
  • 30
    • 84856545857 scopus 로고    scopus 로고
    • Projective synchronization of different fractional-order chaotic systems with non-identical orders
    • MR2891007 ZBL1257.34040 2-s2.0-84856545857 10.1016/j.nonrwa.2011.12.006
    • Si G., Sun Z., Zhang Y., Chen W., Projective synchronization of different fractional-order chaotic systems with non-identical orders. Nonlinear Analysis: Real World Applications 2012 13 4 1761 1771 MR2891007 ZBL1257.34040 2-s2.0-84856545857 10.1016/j.nonrwa.2011.12.006
    • (2012) Nonlinear Analysis: Real World Applications , vol.13 , Issue.4 , pp. 1761-1771
    • Si, G.1    Sun, Z.2    Zhang, Y.3    Chen, W.4
  • 31
    • 0037081673 scopus 로고    scopus 로고
    • Analysis of fractional differential equations
    • MR1876137 ZBL1014.34003 2-s2.0-0037081673 10.1006/jmaa.2000.7194
    • Diethelm K., Ford N. J., Analysis of fractional differential equations. Journal of Mathematical Analysis and Applications 2002 265 2 229 248 MR1876137 ZBL1014.34003 2-s2.0-0037081673 10.1006/jmaa.2000.7194
    • (2002) Journal of Mathematical Analysis and Applications , vol.265 , Issue.2 , pp. 229-248
    • Diethelm, K.1    Ford, N.J.2
  • 32
    • 33947133956 scopus 로고    scopus 로고
    • Stability analysis of linear fractional differential system with multiple time delays
    • DOI 10.1007/s11071-006-9094-0
    • Deng W., Li C., Lü J., Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dynamics 2007 48 4 409 416 MR2312588 ZBL1185.34115 2-s2.0-33947133956 10.1007/s11071-006-9094-0 (Pubitemid 46407957)
    • (2007) Nonlinear Dynamics , vol.48 , Issue.4 , pp. 409-416
    • Deng, W.1    Li, C.2    Lu, J.3
  • 33
    • 51249088596 scopus 로고    scopus 로고
    • Chaotic attractors in incommensurate fractional order systems
    • MR2514122 ZBL1157.26310 2-s2.0-51249088596 10.1016/j.physd.2008.03.037
    • Tavazoei M. S., Haeri M., Chaotic attractors in incommensurate fractional order systems. Physica D 2008 237 20 2628 2637 MR2514122 ZBL1157.26310 2-s2.0-51249088596 10.1016/j.physd.2008.03.037
    • (2008) Physica D , vol.237 , Issue.20 , pp. 2628-2637
    • Tavazoei, M.S.1    Haeri, M.2
  • 34
    • 84864407494 scopus 로고    scopus 로고
    • Parameter estimation and topology identification of uncertain fractional order complex networks
    • 10.1016/j.cnsns.2012.05.005
    • Si G., Sun Z., Zhang H., Zhang Y., Parameter estimation and topology identification of uncertain fractional order complex networks. CommuNications in Nonlinear Science and Numerical Simulation 2012 17 12 5158 5171 10.1016/j.cnsns.2012.05.005
    • (2012) CommuNications in Nonlinear Science and Numerical Simulation , vol.17 , Issue.12 , pp. 5158-5171
    • Si, G.1    Sun, Z.2    Zhang, H.3    Zhang, Y.4
  • 35
    • 84864407494 scopus 로고    scopus 로고
    • Parameter estimation and topology identification of uncertain fractional order complex networks
    • 10.1016/j.cnsns.2012.05.005
    • Si G., Sun Z., Zhang H., Zhang Y., Parameter estimation and topology identification of uncertain fractional order complex networks. Communications in Nonlinear Science and Numerical Simulation 2012 17 12 5158 5171 10.1016/j.cnsns.2012.05.005
    • (2012) Communications in Nonlinear Science and Numerical Simulation , vol.17 , Issue.12 , pp. 5158-5171
    • Si, G.1    Sun, Z.2    Zhang, H.3    Zhang, Y.4
  • 36
    • 84888367355 scopus 로고    scopus 로고
    • Inversion mechanism with functional extrema model for identification incommensurate and hyper fractional chaos via differential evolution
    • S0957417413007082 10.1016/j.eswa.2013.08.087
    • Gao F., Fei F.-X., Lee X.-J., Tong H.-Q., Deng Y.-F., Zhao H.-L., Inversion mechanism with functional extrema model for identification incommensurate and hyper fractional chaos via differential evolution. Expert Systems with Applications 2014 41 4(2) 1915 1927 S0957417413007082 10.1016/j.eswa.2013.08.087
    • (2014) Expert Systems with Applications , vol.41 , Issue.42 , pp. 1915-1927
    • Gao, F.1    Fei, F.-X.2    Lee, X.-J.3    Tong, H.-Q.4    Deng, Y.-F.5    Zhao, H.-L.6
  • 39
    • 84875708493 scopus 로고    scopus 로고
    • Multiobjective cuckoo search for design optimization
    • 10.1016/j.cor.2011.09.026 MR3041434
    • Yang X.-S., Deb S., Multiobjective cuckoo search for design optimization. Computers & Operations Research 2013 40 6 1616 1624 10.1016/j.cor.2011.09. 026 MR3041434
    • (2013) Computers & Operations Research , vol.40 , Issue.6 , pp. 1616-1624
    • Yang, X.-S.1    Deb, S.2
  • 40
    • 69749102394 scopus 로고    scopus 로고
    • On the fractional Adams method
    • MR2562405 ZBL1189.65142 2-s2.0-69749102394 10.1016/j.camwa.2009.07.050
    • Li C., Tao C., On the fractional Adams method. Computers and Mathematics with Applications 2009 58 8 1573 1588 MR2562405 ZBL1189.65142 2-s2.0-69749102394 10.1016/j.camwa.2009.07.050
    • (2009) Computers and Mathematics with Applications , vol.58 , Issue.8 , pp. 1573-1588
    • Li, C.1    Tao, C.2
  • 41
    • 80051704994 scopus 로고    scopus 로고
    • An efficient parallel algorithm for the numerical solution of fractional differential equations
    • MR2837642 ZBL06217556 2-s2.0-80051704994 10.2478/s13540-011-0029-1
    • Diethelm K., An efficient parallel algorithm for the numerical solution of fractional differential equations. Fractional Calculus and Applied Analysis 2011 14 3 475 490 MR2837642 ZBL06217556 2-s2.0-80051704994 10.2478/s13540-011- 0029-1
    • (2011) Fractional Calculus and Applied Analysis , vol.14 , Issue.3 , pp. 475-490
    • Diethelm, K.1
  • 45
    • 0004182814 scopus 로고
    • New York, NY, USA Academic Press Mathematics in Science and Engineering MR0361633
    • Oldham K. B., Spanier J., The Fractional Calculus 1974 111 New York, NY, USA Academic Press xiii+234 Mathematics in Science and Engineering MR0361633
    • (1974) The Fractional Calculus , vol.111
    • Oldham, K.B.1    Spanier, J.2
  • 47
    • 85106205448 scopus 로고    scopus 로고
    • Fractional-order chaotic systems
    • Berlin, Germany Springer Nonlinear Physical Science 10.1007/978-3-642- 18101-6-5
    • Petráš I., Fractional-order chaotic systems. Fractional-Order Nonlinear Systems 2011 Berlin, Germany Springer 103 184 Nonlinear Physical Science 10.1007/978-3-642-18101-6-5
    • (2011) Fractional-Order Nonlinear Systems , pp. 103-184
    • Petráš, I.1
  • 48
    • 84888363084 scopus 로고    scopus 로고
    • Fractional calculus
    • Berlin, Germany Springer 10.1007/978-3-642-18101-6-2
    • Petráš I., Fractional calculus. Nonlinear Physica 2011 Berlin, Germany Springer 7 42 10.1007/978-3-642-18101-6-2
    • (2011) Nonlinear Physica , pp. 7-42
    • Petráš, I.1
  • 52
    • 84855986175 scopus 로고    scopus 로고
    • A new multi-gene genetic programming approach to nonlinear system modeling. Part I: Materials and structural engineering problems
    • 2-s2.0-84855986175 10.1007/s00521-011-0734-z
    • Gandomi A. H., Alavi A. H., A new multi-gene genetic programming approach to nonlinear system modeling. Part I: materials and structural engineering problems. Neural Computing & Applications 2012 21 1 171 187 2-s2.0-84855986175 10.1007/s00521-011-0734-z
    • (2012) Neural Computing & Applications , vol.21 , Issue.1 , pp. 171-187
    • Gandomi, A.H.1    Alavi, A.H.2
  • 53
    • 84856002704 scopus 로고    scopus 로고
    • A new multi-gene genetic programming approach to non-linear system modeling. Part II: Geotechnical and earthquake engineering problems
    • 2-s2.0-84856002704 10.1007/s00521-011-0735-y
    • Gandomi A. H., Alavi A. H., A new multi-gene genetic programming approach to non-linear system modeling. Part II: geotechnical and earthquake engineering problems. Neural Computing & Applications 2012 21 1 189 201 2-s2.0-84856002704 10.1007/s00521-011-0735-y
    • (2012) Neural Computing & Applications , vol.21 , Issue.1 , pp. 189-201
    • Gandomi, A.H.1    Alavi, A.H.2
  • 55
    • 27344438605 scopus 로고    scopus 로고
    • A hybrid genetic programming approach for the analytical solution of differential equations
    • DOI 10.1080/03081070500065676
    • Kirstukas S. J., Bryden K. M., Ashlock D. A., A hybrid genetic programming approach for the analytical solution of differential equations. International Journal of General Systems 2005 34 3 279 299 2-s2.0-27344438605 10.1080/03081070500065676 (Pubitemid 41523699)
    • (2005) International Journal of General Systems , vol.34 , Issue.3 , pp. 279-299
    • Kirstukas, S.J.1    Bryden, K.M.2    Ashlock, D.A.3
  • 57
    • 10944230818 scopus 로고    scopus 로고
    • Genetic programming-based chaotic time series modeling
    • DOI 10.1631/jzus.2004.1432
    • Zhang W., Wu Z.-M., Yang G.-K., Genetic programming-based chaotic time series modeling. Journal of Zhejiang University: Science 2004 5 11 1432 1439 2-s2.0-10944230818 10.1631/jzus.2004.1432 (Pubitemid 40017153)
    • (2004) Journal of Zhejiang University: Science , vol.5 , Issue.11 , pp. 1432-1439
    • Zhang, W.1    Wu, Z.-M.2    Yang, G.-K.3
  • 59
    • 0035422824 scopus 로고    scopus 로고
    • Reconstruction of polynomial systems from noisy time-series measurements using genetic programming
    • DOI 10.1109/41.937405, PII S0278004601062748
    • Varadan V., Leung H., Reconstruction of polynomial systems from noisy time-series measurements using genetic programming. IEEE Transactions on Industrial Electronics 2001 48 4 742 748 2-s2.0-0035422824 10.1109/41.937405 (Pubitemid 32780041)
    • (2001) IEEE Transactions on Industrial Electronics , vol.48 , Issue.4 , pp. 742-748
    • Varadan, V.1    Leung, H.2
  • 60
    • 77950243306 scopus 로고    scopus 로고
    • Evolutionary reconstruction of chaotic systems
    • chapter 8 Springer 2-s2.0-77950243306 10.1007/978-3-642-10707-8-8
    • Zelinka I., Raidl A., Evolutionary reconstruction of chaotic systems. Studies in Computational Intelligence 2010 267 chapter 8 Springer 265 291 2-s2.0-77950243306 10.1007/978-3-642-10707-8-8
    • (2010) Studies in Computational Intelligence , vol.267 , pp. 265-291
    • Zelinka, I.1    Raidl, A.2
  • 62
    • 84866147063 scopus 로고    scopus 로고
    • An investigation on evolutionary reconstruction of continuous chaotic systems
    • 2-s2.0-79960556990 10.1016/j.mcm.2011.06.034
    • Zelinka I., Chadli M., Davendra D., Senkerik R., Jasek R., An investigation on evolutionary reconstruction of continuous chaotic systems. Mathematical and Computer Modelling 2011 57 1-2 2 15 2-s2.0-79960556990 10.1016/j.mcm.2011.06.034
    • (2011) Mathematical and Computer Modelling , vol.57 , Issue.1-2 , pp. 2-15
    • Zelinka, I.1    Chadli, M.2    Davendra, D.3    Senkerik, R.4    Jasek, R.5
  • 63
    • 67650080990 scopus 로고    scopus 로고
    • Parameter estimation for chaotic system with initial random noises by particle swarm optimization
    • 2-s2.0-67650080990 10.1016/j.chaos.2009.03.074
    • Gao F., Lee J.-J., Li Z., Tong H., Lü X., Parameter estimation for chaotic system with initial random noises by particle swarm optimization. Chaos, Solitons & Fractals 2009 42 2 1286 1291 2-s2.0-67650080990 10.1016/j.chaos.2009.03.074
    • (2009) Chaos, Solitons & Fractals , vol.42 , Issue.2 , pp. 1286-1291
    • Gao, F.1    Lee, J.-J.2    Li, Z.3    Tong, H.4    Lü, X.5
  • 64
    • 80054917152 scopus 로고    scopus 로고
    • A Novel non-Lyapunov way for detecting uncertain parameters of chaos system with random noises
    • 2-s2.0-80054917152 10.1016/j.eswa.2011.08.076
    • Gao F., Qi Y., Balasingham I., Yin Q., Gao H., A Novel non-Lyapunov way for detecting uncertain parameters of chaos system with random noises. Expert Systems with Applications 2012 39 2 1779 1783 2-s2.0-80054917152 10.1016/j.eswa.2011.08.076
    • (2012) Expert Systems with Applications , vol.39 , Issue.2 , pp. 1779-1783
    • Gao, F.1    Qi, Y.2    Balasingham, I.3    Yin, Q.4    Gao, H.5
  • 65
    • 0042416849 scopus 로고    scopus 로고
    • Parameters identification and control of Lorenz chaotic system
    • Guan X.-P., Peng H.-P., Li L.-X., Wang Y.-Q., Parameters identification and control of Lorenz chaotic system. Acta Physica Sinica 2001 50 1 29 2-s2.0-0042416849 (Pubitemid 33639190)
    • (2001) Wuli Xuebao/Acta Physica Sinica , vol.50 , Issue.1 , pp. 29
    • Guan, X.-P.1    Peng, H.-P.2    Li, L.-X.3    Wang, Y.-Q.4
  • 66
    • 0000186307 scopus 로고    scopus 로고
    • Estimating model parameters from time series by autosynchronization
    • Parlitz U., Estimating model parameters from time series by autosynchronization. Physical Review Letters 1996 76 8 1232 1235 2-s2.0-0000186307 (Pubitemid 126586086)
    • (1996) Physical Review Letters , vol.76 , Issue.8 , pp. 1232-1235
    • Parlitz, U.1
  • 67
    • 29144460641 scopus 로고    scopus 로고
    • Parameters identification of chaotic systems via chaotic ant swarm
    • DOI 10.1016/j.chaos.2005.04.110, PII S0960077905004704
    • Li L., Yang Y., Peng H., Wang X., Parameters identification of chaotic systems via chaotic ant swarm. Chaos, Solitons & Fractals 2006 28 5 1204 1211 2-s2.0-29144460641 10.1016/j.chaos.2005.04.110 (Pubitemid 41815092)
    • (2006) Chaos, Solitons and Fractals , vol.28 , Issue.5 , pp. 1204-1211
    • Li, L.1    Yang, Y.2    Peng, H.3    Wang, X.4
  • 68
    • 33845380385 scopus 로고    scopus 로고
    • Parameter identification of Chen and Lu systems: A differential evolution approach
    • DOI 10.1016/j.chaos.2005.11.067, PII S0960077905011653
    • Chang W.-D., Parameter identification of Chen and Lü systems: a differential evolution approach. Chaos, Solitons & Fractals 2007 32 4 1469 1476 2-s2.0-33845380385 10.1016/j.chaos.2005.11.067 (Pubitemid 44909760)
    • (2007) Chaos, Solitons and Fractals , vol.32 , Issue.4 , pp. 1469-1476
    • Chang, W.-D.1
  • 69
    • 48749116331 scopus 로고    scopus 로고
    • Parameter identification of chaotic systems using evolutionary programming approach
    • 2-s2.0-48749116331 10.1016/j.eswa.2007.09.021
    • Chang J.-F., Yang Y.-S., Liao T.-L., Yan J.-J., Parameter identification of chaotic systems using evolutionary programming approach. Expert Systems with Applications 2008 35 4 2074 2079 2-s2.0-48749116331 10.1016/j.eswa.2007.09.021
    • (2008) Expert Systems with Applications , vol.35 , Issue.4 , pp. 2074-2079
    • Chang, J.-F.1    Yang, Y.-S.2    Liao, T.-L.3    Yan, J.-J.4
  • 70
    • 42449109885 scopus 로고    scopus 로고
    • Parameters estimation online for Lorenz system by a novel quantum-behaved particle swarm optimization
    • DOI 10.1088/1674-1056/17/4/008
    • Gao F., Li Z.-Q., Tong H.-Q., Parameters estimation online for Lorenz system by a novel quantum-behaved particle swarm optimization. Chinese Physics B 2008 17 4 1196 1201 2-s2.0-42449109885 10.1088/1674-1056/17/4/008 (Pubitemid 351571754)
    • (2008) Chinese Physics B , vol.17 , Issue.4 , pp. 1196-1201
    • Gao, F.1    Li, Z.-Q.2    Tong, H.-Q.3
  • 71
    • 33644651335 scopus 로고    scopus 로고
    • Parameter estimation for chaotic system based on particle swarm optimization
    • Gao F., Tong H.-Q., Parameter estimation for chaotic system based on particle swarm optimization. Acta Physica Sinica 2006 55 2 577 582 2-s2.0-33644651335 (Pubitemid 43322814)
    • (2006) Wuli Xuebao/Acta Physica Sinica , vol.55 , Issue.2 , pp. 577-582
    • Gao, F.1    Tong, H.-Q.2
  • 72
    • 41849151474 scopus 로고    scopus 로고
    • Robust synchronization and parameter identification on a class of uncertain chaotic systems
    • DOI 10.1016/j.chaos.2006.10.042, PII S0960077906010228
    • Shen L., Wang M., Robust synchronization and parameter identification on a class of uncertain chaotic systems. Chaos, Solitons & Fractals 2008 38 1 106 111 2-s2.0-41849151474 10.1016/j.chaos.2006.10.042 (Pubitemid 351503971)
    • (2008) Chaos, Solitons and Fractals , vol.38 , Issue.1 , pp. 106-111
    • Shen, L.1    Wang, M.2
  • 73
    • 74849126061 scopus 로고    scopus 로고
    • Parameters identification of chaotic systems by quantum-behaved particle swarm optimization
    • MR2597373 ZBL1181.65103 2-s2.0-74849126061 10.1080/00207160903029802
    • Yang K., Maginu K., Nomura H., Parameters identification of chaotic systems by quantum-behaved particle swarm optimization. International Journal of Computer Mathematics 2009 86 12 2225 2235 MR2597373 ZBL1181.65103 2-s2.0-74849126061 10.1080/00207160903029802
    • (2009) International Journal of Computer Mathematics , vol.86 , Issue.12 , pp. 2225-2235
    • Yang, K.1    Maginu, K.2    Nomura, H.3
  • 74
    • 81255161195 scopus 로고    scopus 로고
    • Solving problems in chaos control though an differential evolution algorithm with region zooming
    • 2-s2.0-81255161195 10.4028/www.scientific.net/AMM.110-116.5048
    • Gao F., Qi Y., Yin Q., Xiao J., Solving problems in chaos control though an differential evolution algorithm with region zooming. Applied Mechanics and Materials 2012 110-116 5048 5056 2-s2.0-81255161195 10.4028/www.scientific.net/ AMM.110-116.5048
    • (2012) Applied Mechanics and Materials , vol.110-116 , pp. 5048-5056
    • Gao, F.1    Qi, Y.2    Yin, Q.3    Xiao, J.4
  • 75
    • 84865008072 scopus 로고    scopus 로고
    • A novel artificial bee colony algorithm with space contraction for unknown parameters identification and time-delays of chaotic systems
    • 10.1016/j.amc.2012.06.040
    • Gao F., Fei F.-X., Xu Q., Deng Y.-F., Qi Y.-B., Balasingham I., A novel artificial bee colony algorithm with space contraction for unknown parameters identification and time-delays of chaotic systems. Applied Mathematics and Computation 2012 219 2 552 568 10.1016/j.amc.2012.06.040
    • (2012) Applied Mathematics and Computation , vol.219 , Issue.2 , pp. 552-568
    • Gao, F.1    Fei, F.-X.2    Xu, Q.3    Deng, Y.-F.4    Qi, Y.-B.5    Balasingham, I.6
  • 77
    • 33646366905 scopus 로고    scopus 로고
    • Chaotic dynamics of the fractional-order Lu system and its synchronization
    • DOI 10.1016/j.physleta.2006.01.068, PII S0375960106001551
    • Lu J. G., Chaotic dynamics of the fractional-order Lü system and its synchronization. Physics Letters A 2006 354 4 305 311 2-s2.0-33646366905 10.1016/j.physleta.2006.01.068 (Pubitemid 43668647)
    • (2006) Physics Letters, Section A: General, Atomic and Solid State Physics , vol.354 , Issue.4 , pp. 305-311
    • Lu, J.G.1
  • 78
    • 2042470796 scopus 로고    scopus 로고
    • Chaos in the fractional order Chen system and its control
    • 2-s2.0-2042470796 10.1016/j.chaos.2004.02.035
    • Li C., Chen G., Chaos in the fractional order Chen system and its control. Chaos, Solitons & Fractals 2004 22 3 549 554 2-s2.0-2042470796 10.1016/j.chaos.2004.02.035
    • (2004) Chaos, Solitons & Fractals , vol.22 , Issue.3 , pp. 549-554
    • Li, C.1    Chen, G.2
  • 79
    • 0142000477 scopus 로고    scopus 로고
    • Differential Evolution - A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces
    • Storn R., Price K., Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 1997 11 4 341 359 MR1479553 ZBL0888.90135 2-s2.0-0142000477 (Pubitemid 127502202)
    • (1997) Journal of Global Optimization , vol.11 , Issue.4 , pp. 341-359
    • Storn, R.1    Price, K.2
  • 80
    • 79951644739 scopus 로고    scopus 로고
    • Computing two linchpins of topological degree by a novel differential evolution algorithm
    • Gao F., Tong H., Computing two linchpins of topological degree by a novel differential evolution algorithm. International Journal of Computational Intelligence and Applications 2005 5 3 335 350
    • (2005) International Journal of Computational Intelligence and Applications , vol.5 , Issue.3 , pp. 335-350
    • Gao, F.1    Tong, H.2
  • 81
    • 18744396943 scopus 로고    scopus 로고
    • Computing unstable Period orbits of discrete chaotic system though differential evolutionary algorithms basing on elite subspace
    • Gao F., Computing unstable Period orbits of discrete chaotic system though differential evolutionary algorithms basing on elite subspace. System Engineering Theory and Practice 2005 25 4 96 102 2-s2.0-18744396943 (Pubitemid 40668784)
    • (2005) Xitong Gongcheng Lilun yu Shijian/System Engineering Theory and Practice , vol.25 , Issue.4 , pp. 96-102
    • Gao, F.1
  • 82
    • 78049290320 scopus 로고    scopus 로고
    • A 2-Opt based differential evolution for global optimization
    • 2-s2.0-78049290320 10.1016/j.asoc.2010.05.012
    • Chiang C.-W., Lee W.-P., Heh J.-S., A 2-Opt based differential evolution for global optimization. Applied Soft Computing Journal 2010 10 4 1200 1207 2-s2.0-78049290320 10.1016/j.asoc.2010.05.012
    • (2010) Applied Soft Computing Journal , vol.10 , Issue.4 , pp. 1200-1207
    • Chiang, C.-W.1    Lee, W.-P.2    Heh, J.-S.3
  • 84
    • 19144371559 scopus 로고    scopus 로고
    • Chaotic dynamics and synchronization of fractional-order Arneodo's systems
    • DOI 10.1016/j.chaos.2005.02.023, PII S0960077905001967
    • Lu J. G., Chaotic dynamics and synchronization of fractional-order Arneodo's systems. Chaos, Solitons & Fractals 2005 26 4 1125 1133 2-s2.0-19144371559 10.1016/j.chaos.2005.02.023 (Pubitemid 40715537)
    • (2005) Chaos, Solitons and Fractals , vol.26 , Issue.4 , pp. 1125-1133
    • Lu, J.G.1
  • 85
    • 23744466023 scopus 로고    scopus 로고
    • Chaotic dynamics and synchronization of fractional-order Genesio-Tesi systems
    • DOI 10.1088/1009-1963/14/8/007
    • Lu J.-G., Chaotic dynamics and synchronization of fractional-order Genesio-Tesi systems. Chinese Physics 2005 14 8 1517 1521 2-s2.0-23744466023 10.1088/1009-1963/14/8/007 (Pubitemid 41118297)
    • (2005) Chinese Physics , vol.14 , Issue.8 , pp. 1517-1521
    • Lu, J.-G.1
  • 86
    • 41849104190 scopus 로고    scopus 로고
    • A note on the fractional-order Chua's system
    • DOI 10.1016/j.chaos.2006.10.054, PII S0960077906010290
    • Petráš I., A note on the fractional-order Chua's system. Chaos, Solitons & Fractals 2008 38 1 140 147 2-s2.0-41849104190 10.1016/j.chaos.2006.10.054 (Pubitemid 351503975)
    • (2008) Chaos, Solitons and Fractals , vol.38 , Issue.1 , pp. 140-147
    • Petras, I.1
  • 87
    • 77952524788 scopus 로고    scopus 로고
    • Adaptive tracking control and synchronization of fractional hyper-chaotic Lorenz system with unknown parameters
    • 2-s2.0-77952524788
    • Zhao L.-D., Hu J.-B., Liu X.-H., Adaptive tracking control and synchronization of fractional hyper-chaotic Lorenz system with unknown parameters. Acta Physica Sinica 2010 59 4 2305 2309 2-s2.0-77952524788
    • (2010) Acta Physica Sinica , vol.59 , Issue.4 , pp. 2305-2309
    • Zhao, L.-D.1    Hu, J.-B.2    Liu, X.-H.3
  • 88
    • 65249180157 scopus 로고    scopus 로고
    • Circuit implementation and tracking control of the fractional-order hyper-chaotic Lü system
    • 2-s2.0-65249180157
    • Min F.-H., Yu Y., Ge C.-J., Circuit implementation and tracking control of the fractional-order hyper-chaotic Lü system. Acta Physica Sinica 2009 58 3 1456 1461 2-s2.0-65249180157
    • (2009) Acta Physica Sinica , vol.58 , Issue.3 , pp. 1456-1461
    • Min, F.-H.1    Yu, Y.2    Ge, C.-J.3
  • 89
    • 56349131727 scopus 로고    scopus 로고
    • A hyperchaotic system and its fractional order circuit simulation
    • Liu C.-X., A hyperchaotic system and its fractional order circuit simulation. Acta Physica Sinica 2007 56 12 6865 6873
    • (2007) Acta Physica Sinica , vol.56 , Issue.12 , pp. 6865-6873
    • Liu, C.-X.1
  • 90
    • 84863386967 scopus 로고    scopus 로고
    • Synchronization for fractional order hyperchaotic chen system and fractional order hyperchaotic rössler system with different structure
    • 050502
    • Li D., Deng L.-M., Du Y.-X., Yang Y.-Y., Synchronization for fractional order hyperchaotic chen system and fractional order hyperchaotic rössler system with different structure. Acta Physica Sinica 2012 61 5 050502
    • (2012) Acta Physica Sinica , vol.61 , Issue.5
    • Li, D.1    Deng, L.-M.2    Du, Y.-X.3    Yang, Y.-Y.4
  • 91
    • 84863348089 scopus 로고    scopus 로고
    • Modified adaptive controller for synchronization of incommensurate fractional-order chaotic systems
    • 2-s2.0-84858304325 10.1088/1674-1056/21/3/030505 030505
    • Zhang R.-X., Yang S.-P., Modified adaptive controller for synchronization of incommensurate fractional-order chaotic systems. Chinese Physics B 2012 21 3 2-s2.0-84858304325 10.1088/1674-1056/21/3/030505 030505
    • (2012) Chinese Physics B , vol.21 , Issue.3
    • Zhang, R.-X.1    Yang, S.-P.2
  • 92
    • 84855761900 scopus 로고    scopus 로고
    • Four-wing hyperchaotic attractor generated from a new 4D system with one equilibrium and its fractional-order form
    • MR2870579 ZBL1245.34054 2-s2.0-84855761900 10.1007/s11071-011-0060-0
    • Dadras S., Momeni H. R., Qi G., Wang Z.-L., Four-wing hyperchaotic attractor generated from a new 4D system with one equilibrium and its fractional-order form. Nonlinear Dynamics 2012 67 2 1161 1173 MR2870579 ZBL1245.34054 2-s2.0-84855761900 10.1007/s11071-011-0060-0
    • (2012) Nonlinear Dynamics , vol.67 , Issue.2 , pp. 1161-1173
    • Dadras, S.1    Momeni, H.R.2    Qi, G.3    Wang, Z.-L.4


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