메뉴 건너뛰기




Volumn 17, Issue 1, 2012, Pages 305-316

Parameter identification and synchronization of fractional-order chaotic systems

Author keywords

Active control; Caputo fractional derivative; Chaos synchronization; Fractional order chaotic systems; Particle swarm optimization

Indexed keywords

CHAOS CONTROL; CHAOTIC SYSTEMS; DIFFERENTIATION (CALCULUS); PARAMETER ESTIMATION; PARTICLE SWARM OPTIMIZATION (PSO);

EID: 79961020785     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2011.04.005     Document Type: Article
Times cited : (98)

References (48)
  • 1
    • 33747375809 scopus 로고    scopus 로고
    • An effective hybrid PSOSA strategy for optimization and its application to parameter estimation
    • Li L., Wang L., Liu L. An effective hybrid PSOSA strategy for optimization and its application to parameter estimation. Appl Math Comput 2006, 179:135-146.
    • (2006) Appl Math Comput , vol.179 , pp. 135-146
    • Li, L.1    Wang, L.2    Liu, L.3
  • 2
    • 65349191196 scopus 로고    scopus 로고
    • Parameter estimation for time-delay chaotic system by particle swarm optimization
    • Tang Y., Guan X. Parameter estimation for time-delay chaotic system by particle swarm optimization. Chaos Solitons Fract 2009, 40:1391-1398.
    • (2009) Chaos Solitons Fract , vol.40 , pp. 1391-1398
    • Tang, Y.1    Guan, X.2
  • 3
    • 73249126274 scopus 로고    scopus 로고
    • Parameter identification of chaotic dynamics systems through an improved particle swarm optimization
    • Modares H., Alfi A., Fateh M. Parameter identification of chaotic dynamics systems through an improved particle swarm optimization. Expert Syst Appl 2010, 37:3714-3720.
    • (2010) Expert Syst Appl , vol.37 , pp. 3714-3720
    • Modares, H.1    Alfi, A.2    Fateh, M.3
  • 4
    • 34147175619 scopus 로고    scopus 로고
    • Parameter estimation for chaotic systems by particle swarm optimization
    • He Q., Wang L., Liu B. Parameter estimation for chaotic systems by particle swarm optimization. Chaos Solitons Fract 2007, 34:654-661.
    • (2007) Chaos Solitons Fract , vol.34 , pp. 654-661
    • He, Q.1    Wang, L.2    Liu, B.3
  • 5
    • 67651211709 scopus 로고    scopus 로고
    • Parameter estimation of chaotic system with time-delay: A differential evolution approach
    • Tang Y., Guan X. Parameter estimation of chaotic system with time-delay: A differential evolution approach. Chaos Solitons Fract 2009, 42:3132-3139.
    • (2009) Chaos Solitons Fract , vol.42 , pp. 3132-3139
    • Tang, Y.1    Guan, X.2
  • 6
    • 33845380385 scopus 로고    scopus 로고
    • Parameter identification of Chen and Lü systems: A differential evolution approach
    • Chang W. Parameter identification of Chen and Lü systems: A differential evolution approach. Chaos Solitons Fract 2007, 32:1469-1476.
    • (2007) Chaos Solitons Fract , vol.32 , pp. 1469-1476
    • Chang, W.1
  • 7
    • 33645884120 scopus 로고    scopus 로고
    • Parameter identification of Rossler's chaotic system by an evolutionary algorithm
    • Chang W. Parameter identification of Rossler's chaotic system by an evolutionary algorithm. Chaos Solitons Fract 2006, 29:1047-1053.
    • (2006) Chaos Solitons Fract , vol.29 , pp. 1047-1053
    • Chang, W.1
  • 8
    • 33845217928 scopus 로고    scopus 로고
    • Parameters identification and adaptive full state hybrid projective synchronization of chaotic (hyper-chaotic) systems
    • Hu M., Xu Z., Zhang R., Hu A. Parameters identification and adaptive full state hybrid projective synchronization of chaotic (hyper-chaotic) systems. Phys Lett A 2007, 361:231-237.
    • (2007) Phys Lett A , vol.361 , pp. 231-237
    • Hu, M.1    Xu, Z.2    Zhang, R.3    Hu, A.4
  • 9
    • 21244504159 scopus 로고    scopus 로고
    • Parameters identification and adaptive synchronization of chaotic systems with unknown parameters
    • Huang L., Wang M., Feng R. Parameters identification and adaptive synchronization of chaotic systems with unknown parameters. Phys Lett A 2005, 342:299-304.
    • (2005) Phys Lett A , vol.342 , pp. 299-304
    • Huang, L.1    Wang, M.2    Feng, R.3
  • 10
    • 42949128019 scopus 로고    scopus 로고
    • Adaptive synchronization of a class of chaotic systems with uncertain parameters
    • (in Chinese)
    • Zhang R., Tian G., Li P., Yang S. Adaptive synchronization of a class of chaotic systems with uncertain parameters. Acta Phys Sin 2008, 57:2073-2080. (in Chinese).
    • (2008) Acta Phys Sin , vol.57 , pp. 2073-2080
    • Zhang, R.1    Tian, G.2    Li, P.3    Yang, S.4
  • 11
    • 62649089138 scopus 로고    scopus 로고
    • Adaptive generalized projective synchronization of two different chaotic systems with unknown parameters
    • Zhang R., Yang S. Adaptive generalized projective synchronization of two different chaotic systems with unknown parameters. Chin Phys B 2008, 17:4073-4079.
    • (2008) Chin Phys B , vol.17 , pp. 4073-4079
    • Zhang, R.1    Yang, S.2
  • 12
    • 71649110871 scopus 로고    scopus 로고
    • Optimize design of adaptive synchronization controllers and parameter observers in different hyperchaotic systems
    • Ma J., Zhang A., Xia Y., Zhang L. Optimize design of adaptive synchronization controllers and parameter observers in different hyperchaotic systems. Appl Math Comput 2010, 215:3318-3326.
    • (2010) Appl Math Comput , vol.215 , pp. 3318-3326
    • Ma, J.1    Zhang, A.2    Xia, Y.3    Zhang, L.4
  • 13
    • 77951427239 scopus 로고    scopus 로고
    • Optimization of self-adaptive synchronization and parameters estimation in chaotic Hindmarsh-Rose neuron model
    • (in Chinese)
    • Ma J., Su W., Gao J. Optimization of self-adaptive synchronization and parameters estimation in chaotic Hindmarsh-Rose neuron model. Acta Phys Sin 2010, 59:1554-1561. (in Chinese).
    • (2010) Acta Phys Sin , vol.59 , pp. 1554-1561
    • Ma, J.1    Su, W.2    Gao, J.3
  • 14
    • 79951579980 scopus 로고    scopus 로고
    • Synchronization of two different uncertain chaotic systems with unknown parameters using a robust adaptive sliding mode controller
    • Pourmahmood M., Khanmohammadi S., Alizadeh G. Synchronization of two different uncertain chaotic systems with unknown parameters using a robust adaptive sliding mode controller. Commun Nonlinear Sci Numer Simul 2011, 16:2869-2879.
    • (2011) Commun Nonlinear Sci Numer Simul , vol.16 , pp. 2869-2879
    • Pourmahmood, M.1    Khanmohammadi, S.2    Alizadeh, G.3
  • 15
    • 77955018368 scopus 로고    scopus 로고
    • Bifurcations of fractional-order diffusionless Lorenz system
    • Sun K., Sprott J. Bifurcations of fractional-order diffusionless Lorenz system. Electronic J Theor Phys 2009, 22:123-134.
    • (2009) Electronic J Theor Phys , vol.22 , pp. 123-134
    • Sun, K.1    Sprott, J.2
  • 16
    • 3342927052 scopus 로고    scopus 로고
    • Chaos and hyperchaos in the fractional-order Rössler equations
    • Li C., Cheng G. Chaos and hyperchaos in the fractional-order Rössler equations. Physica A 2004, 341:55-61.
    • (2004) Physica A , vol.341 , pp. 55-61
    • Li, C.1    Cheng, G.2
  • 17
    • 1842832060 scopus 로고    scopus 로고
    • Chaos in Chen's system with a fractional order
    • Li C., Peng G. Chaos in Chen's system with a fractional order. Chaos Solitons Fract 2004, 22:443-450.
    • (2004) Chaos Solitons Fract , vol.22 , pp. 443-450
    • Li, C.1    Peng, G.2
  • 18
    • 23144435914 scopus 로고    scopus 로고
    • A note on the fractional-order Chen system
    • Lu J., Chen G. A note on the fractional-order Chen system. Chaos Solitons Fract 2006, 27:685-688.
    • (2006) Chaos Solitons Fract , vol.27 , pp. 685-688
    • Lu, J.1    Chen, G.2
  • 19
    • 0041384356 scopus 로고    scopus 로고
    • Chaotic dynamics of the fractional Lorenz system
    • Grigorenko I., Grigorenko E. Chaotic dynamics of the fractional Lorenz system. Phys Rev Lett 2003, 91:034101.
    • (2003) Phys Rev Lett , vol.91 , pp. 034101
    • Grigorenko, I.1    Grigorenko, E.2
  • 20
    • 67649861441 scopus 로고    scopus 로고
    • Dynamic analysis of a fractional-Lorenz chaotic system
    • Yu Y., Li H., Wang S., Yu J. Dynamic analysis of a fractional-Lorenz chaotic system. Chaos Solitons Fract 2009, 42:1181-1189.
    • (2009) Chaos Solitons Fract , vol.42 , pp. 1181-1189
    • Yu, Y.1    Li, H.2    Wang, S.3    Yu, J.4
  • 21
    • 70449574688 scopus 로고    scopus 로고
    • Chaos in the fractional-order Lorenz system
    • Wu X., Shen S. Chaos in the fractional-order Lorenz system. Int J Comput Math 2009, 86:1274-1282.
    • (2009) Int J Comput Math , vol.86 , pp. 1274-1282
    • Wu, X.1    Shen, S.2
  • 22
    • 77952741594 scopus 로고    scopus 로고
    • Chaos in fractional conjugate Lorenz system and its scaling attractors
    • Yang Q., Zeng C. Chaos in fractional conjugate Lorenz system and its scaling attractors. Commun Nonlinear Sci Numer Simul 2010, 15:4041-4051.
    • (2010) Commun Nonlinear Sci Numer Simul , vol.15 , pp. 4041-4051
    • Yang, Q.1    Zeng, C.2
  • 24
    • 74149087189 scopus 로고    scopus 로고
    • Chaos in fractional ordered Liu system
    • Varsha D., Sachin B. Chaos in fractional ordered Liu system. Comput Math Appl 2010, 59:1117-1127.
    • (2010) Comput Math Appl , vol.59 , pp. 1117-1127
    • Varsha, D.1    Sachin, B.2
  • 25
    • 0036650479 scopus 로고    scopus 로고
    • A predictor-corrector approach for the numerical solution of fractional differential equations
    • Diethelm K., Ford N., Freed A. A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dyn 2002, 29:3-22.
    • (2002) Nonlinear Dyn , vol.29 , pp. 3-22
    • Diethelm, K.1    Ford, N.2    Freed, A.3
  • 26
    • 0002731965 scopus 로고    scopus 로고
    • Stability results for fractional differential equations with applications to control processing.
    • In: IEEE-SMC Proceedings on Computational Engineering in Systems and Application Multi-Conference, IMACS, Lille, France
    • Matignon D. Stability results for fractional differential equations with applications to control processing. In: IEEE-SMC Proceedings on Computational Engineering in Systems and Application Multi-Conference, vol. 2, IMACS, Lille, France, 1996, p. 963-8.
    • (1996) , vol.2 , pp. 963-968
    • Matignon, D.1
  • 27
    • 51249088596 scopus 로고    scopus 로고
    • Chaotic attractors in incommensurate fractional order systems
    • Tavazoei M., Haeri M. Chaotic attractors in incommensurate fractional order systems. Physcia D 2008, 237:2628-2637.
    • (2008) Physcia D , vol.237 , pp. 2628-2637
    • Tavazoei, M.1    Haeri, M.2
  • 28
    • 34347330038 scopus 로고    scopus 로고
    • A necessary condition for double scroll attractor existence in fractional-order systems
    • Tavazoei M., Haeri M. A necessary condition for double scroll attractor existence in fractional-order systems. Phys Lett A 2007, 367:102-113.
    • (2007) Phys Lett A , vol.367 , pp. 102-113
    • Tavazoei, M.1    Haeri, M.2
  • 29
    • 33846056956 scopus 로고    scopus 로고
    • Design of multidirectional multi-scroll chaotic attractors based on fractional differential systems via switching control
    • Deng W., Lü J. Design of multidirectional multi-scroll chaotic attractors based on fractional differential systems via switching control. Chaos 2006, 16:043120.
    • (2006) Chaos , vol.16 , pp. 043120
    • Deng, W.1    Lü, J.2
  • 30
    • 34548617848 scopus 로고    scopus 로고
    • Generating multidirectional multi-scroll chaotic attractors via a fractional differential hysteresis system
    • Deng W., Lü J. Generating multidirectional multi-scroll chaotic attractors via a fractional differential hysteresis system. Phys Lett A 2007, 369:438-443.
    • (2007) Phys Lett A , vol.369 , pp. 438-443
    • Deng, W.1    Lü, J.2
  • 31
    • 0037081673 scopus 로고    scopus 로고
    • Analysis of fractional differential equations
    • Diethelm K., Ford J. Analysis of fractional differential equations. J Math Anal Appl 2002, 265:229-248.
    • (2002) J Math Anal Appl , vol.265 , pp. 229-248
    • Diethelm, K.1    Ford, J.2
  • 32
    • 33947133956 scopus 로고    scopus 로고
    • Stability analysis of linear fractional differential system with multiple time delays
    • Deng W., Li C., Lü J. Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dyn 2007, 48:409-416.
    • (2007) Nonlinear Dyn , vol.48 , pp. 409-416
    • Deng, W.1    Li, C.2    Lü, J.3
  • 33
    • 77951575404 scopus 로고    scopus 로고
    • Synchronization of chaotic fractional-order systems via linear control
    • Odibat Z., Corson N., Aziz-Alaoui M., Bertelle C. Synchronization of chaotic fractional-order systems via linear control. Int J Bifurcat chaos 2010, 20:81-97.
    • (2010) Int J Bifurcat chaos , vol.20 , pp. 81-97
    • Odibat, Z.1    Corson, N.2    Aziz-Alaoui, M.3    Bertelle, C.4
  • 34
    • 72649090282 scopus 로고    scopus 로고
    • Chaos synchronization for a class of nonlinear oscillators with fractional order
    • Song L., Yang J., Xu S. Chaos synchronization for a class of nonlinear oscillators with fractional order. Nonlinear Anal-Theor 2010, 72:2326-2336.
    • (2010) Nonlinear Anal-Theor , vol.72 , pp. 2326-2336
    • Song, L.1    Yang, J.2    Xu, S.3
  • 35
    • 77952237940 scopus 로고    scopus 로고
    • Synchronization of different fractional order chaotic systems using active control
    • Bhalekar S., Daftardar-Gejji V. Synchronization of different fractional order chaotic systems using active control. Commun Nonlinear Sci Numer Simul 2010, 15:3536-3546.
    • (2010) Commun Nonlinear Sci Numer Simul , vol.15 , pp. 3536-3546
    • Bhalekar, S.1    Daftardar-Gejji, V.2
  • 36
    • 68949178216 scopus 로고    scopus 로고
    • Chaos in fractional-order generalized Lorenz system and its synchronization circuit simulation
    • Zhang R., Yang S. Chaos in fractional-order generalized Lorenz system and its synchronization circuit simulation. Chin Phys B 2009, 18:3295-3303.
    • (2009) Chin Phys B , vol.18 , pp. 3295-3303
    • Zhang, R.1    Yang, S.2
  • 37
    • 77649265799 scopus 로고    scopus 로고
    • Adaptive synchronisation of fractional-order chaotic systems
    • Zhang R., Yang S. Adaptive synchronisation of fractional-order chaotic systems. Chin Phys B 2010, 19:020510.
    • (2010) Chin Phys B , vol.19 , pp. 020510
    • Zhang, R.1    Yang, S.2
  • 38
    • 41849090145 scopus 로고    scopus 로고
    • Chaos in the fractional order unified system and its synchronization
    • Wu X., Li J., Chen G. Chaos in the fractional order unified system and its synchronization. J Frank Instit 2008, 345:392-401.
    • (2008) J Frank Instit , vol.345 , pp. 392-401
    • Wu, X.1    Li, J.2    Chen, G.3
  • 39
    • 70350521756 scopus 로고    scopus 로고
    • Adaptive synchronization of the fractional-order unified chaotic system
    • (in Chinese)
    • Zhang R., Yang Y., Yang S. Adaptive synchronization of the fractional-order unified chaotic system. Acta Phys Sin 2009, 58:6039-6044. (in Chinese).
    • (2009) Acta Phys Sin , vol.58 , pp. 6039-6044
    • Zhang, R.1    Yang, Y.2    Yang, S.3
  • 40
    • 18844427587 scopus 로고    scopus 로고
    • Chaos synchronization of the fractional Lü system
    • Deng W., Li C. Chaos synchronization of the fractional Lü system. Physica A 2005, 353:61-72.
    • (2005) Physica A , vol.353 , pp. 61-72
    • Deng, W.1    Li, C.2
  • 41
    • 67249140258 scopus 로고    scopus 로고
    • A fractional-order hyperchaotic system and its synchronization
    • Deng H., Li T., Wang Q., Li H. A fractional-order hyperchaotic system and its synchronization. Chaos Solitons Fract 2009, 41:962-969.
    • (2009) Chaos Solitons Fract , vol.41 , pp. 962-969
    • Deng, H.1    Li, T.2    Wang, Q.3    Li, H.4
  • 42
    • 27744554781 scopus 로고    scopus 로고
    • Chaos synchronization of the Chua system with a fractional order
    • Li C., Deng W., Xu D. Chaos synchronization of the Chua system with a fractional order. Physica A 2006, 360:171-185.
    • (2006) Physica A , vol.360 , pp. 171-185
    • Li, C.1    Deng, W.2    Xu, D.3
  • 44
    • 0029535737 scopus 로고
    • Particle swarm optimization.
    • In: Proc IEEE Int Conf Neural Networks
    • Kennedy J, Eberhart R. Particle swarm optimization. In: Proc IEEE Int Conf Neural Networks, vol. 4, 1995, p. 1942-8.
    • (1995) , vol.4 , pp. 1942-1948
    • Kennedy, J.1    Eberhart, R.2
  • 46
    • 35248862588 scopus 로고    scopus 로고
    • An improved particle swarm optimization algorithm
    • Jiang Y., Hu T., Huang C., Wu X. An improved particle swarm optimization algorithm. Appl Math Comput 2007, 193:231-239.
    • (2007) Appl Math Comput , vol.193 , pp. 231-239
    • Jiang, Y.1    Hu, T.2    Huang, C.3    Wu, X.4
  • 47
    • 77952242081 scopus 로고    scopus 로고
    • PID controller design of nonlinear systems using an improved particle swarm optimization approach
    • Chang W., Shih S. PID controller design of nonlinear systems using an improved particle swarm optimization approach. Commun Nonlinear Sci Numer Simul 2010, 15:3632-3639.
    • (2010) Commun Nonlinear Sci Numer Simul , vol.15 , pp. 3632-3639
    • Chang, W.1    Shih, S.2
  • 48
    • 69549123872 scopus 로고    scopus 로고
    • A novel three-dimensional autonomous chaotic system generating two, three and four-scroll attractors
    • Daras S., Momeni H. A novel three-dimensional autonomous chaotic system generating two, three and four-scroll attractors. Phys Lett A 2009, 373:3637-3642.
    • (2009) Phys Lett A , vol.373 , pp. 3637-3642
    • Daras, S.1    Momeni, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.