메뉴 건너뛰기




Volumn 62, Issue 4, 2010, Pages 851-858

Chaos and hybrid projective synchronization of commensurate and incommensurate fractional-order Chen-Lee systems

Author keywords

Chaos; Chen Lee system; Commensurate; Fractional order system; Hybrid projective synchronization; Incommensurate

Indexed keywords

CHAOS; CHEN-LEE SYSTEM; COMMENSURATE; FRACTIONAL-ORDER SYSTEMS; INCOMMENSURATE; PROJECTIVE SYNCHRONIZATION;

EID: 78049454811     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-010-9767-6     Document Type: Article
Times cited : (69)

References (37)
  • 2
    • 0026124343 scopus 로고
    • Fractional order state equations for the control of viscoelastically damped structures
    • 10.2514/3.20641
    • R.L. Bagley R.A. Calico 1991 Fractional order state equations for the control of viscoelastically damped structures J. Guid. Control Dyn. 14 304 311 10.2514/3.20641
    • (1991) J. Guid. Control Dyn. , vol.14 , pp. 304-311
    • Bagley, R.L.1    Calico, R.A.2
  • 4
    • 0021424253 scopus 로고
    • Linear approximation for transfer function with a pole of fractional order
    • 0532.93025 10.1109/TAC.1984.1103551
    • H.H. Sun A.A. Abdelwahed B. Onaral 1984 Linear approximation for transfer function with a pole of fractional order IEEE Trans. Autom. Control 29 441 444 0532.93025 10.1109/TAC.1984.1103551
    • (1984) IEEE Trans. Autom. Control , vol.29 , pp. 441-444
    • Sun, H.H.1    Abdelwahed, A.A.2    Onaral, B.3
  • 6
    • 0000378977 scopus 로고    scopus 로고
    • Quantum Levy processes and fractional kinetics
    • 10.1103/PhysRevLett.82.1136
    • D. Kunsezov A. Bulagc G.D. Dang 1999 Quantum Levy processes and fractional kinetics Phys. Rev. Lett. 82 1136 1139 10.1103/PhysRevLett.82.1136
    • (1999) Phys. Rev. Lett. , vol.82 , pp. 1136-1139
    • Kunsezov, D.1    Bulagc, A.2    Dang, G.D.3
  • 7
    • 0041384356 scopus 로고    scopus 로고
    • Chaotic dynamics of the fractional Lorenz system
    • 10.1103/PhysRevLett.91.034101
    • I. Grigorenko E. Grigorenko 2003 Chaotic dynamics of the fractional Lorenz system Phys. Rev. Lett. 91 034101 10.1103/PhysRevLett.91.034101
    • (2003) Phys. Rev. Lett. , vol.91 , pp. 034101
    • Grigorenko, I.1    Grigorenko, E.2
  • 8
    • 67649861441 scopus 로고    scopus 로고
    • Dynamic analysis of a fractional-order Lorenz chaotic system
    • 10.1016/j.chaos.2009.03.016 2554825
    • Y. Yu H.X. Li S. Wang J. Yu 2009 Dynamic analysis of a fractional-order Lorenz chaotic system Chaos Solitons Fractals 42 1181 1189 10.1016/j.chaos.2009. 03.016 2554825
    • (2009) Chaos Solitons Fractals , vol.42 , pp. 1181-1189
    • Yu, Y.1    Li, H.X.2    Wang, S.3    Yu, J.4
  • 10
    • 33845466254 scopus 로고    scopus 로고
    • Chaotic dynamics of the fractionally damped Duffing equation
    • DOI 10.1016/j.chaos.2005.11.066, PII S096007790501163X
    • L.J. Sheu H.K. Chen J.H. Chen L.M. Tam 2007 Chaotic dynamics of the fractionally damped duffing equation Chaos Solitons Fractals 31 1459 1468 10.1016/j.chaos.2005.11.066 (Pubitemid 44909759)
    • (2007) Chaos, Solitons and Fractals , vol.32 , Issue.4 , pp. 1459-1468
    • Sheu, L.-J.1    Chen, H.-K.2    Chen, J.-H.3    Tam, L.-M.4
  • 11
    • 34147144036 scopus 로고    scopus 로고
    • Chaos in a fractional order modified Duffing system
    • DOI 10.1016/j.chaos.2005.11.059, PII S0960077905011367
    • Z.M. Ge C.Y. Ou 2007 Chaos in a fractional order modified duffing system Chaos Solitons Fractals 34 262 291 1132.37324 10.1016/j.chaos.2005.11.059 (Pubitemid 46561270)
    • (2007) Chaos, Solitons and Fractals , vol.34 , Issue.2 , pp. 262-291
    • Ge, Z.-M.1    Ou, C.-Y.2
  • 13
    • 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
    • C.P. Li W.H. Deng D. Xu 2006 Chaos synchronization of the Chua system with a fractional order Physica A 360 171 185 10.1016/j.physa.2005.06.078 2186261 (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
  • 14
    • 23144435914 scopus 로고    scopus 로고
    • A note on the fractional-order Chen system
    • DOI 10.1016/j.chaos.2005.04.037, PII S0960077905003590
    • J.G. Lu G. Chen 2006 A note on the fractional-order Chen system Chaos Solitons Fractals 27 685 688 1101.37307 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
  • 15
    • 2042470796 scopus 로고    scopus 로고
    • Chaos in the fractional order Chen system and its control
    • 1069.37025 10.1016/j.chaos.2004.02.035
    • C. Li G. Chen 2004 Chaos in the fractional order Chen system and its control Chaos Solitons Fractals 22 549 554 1069.37025 10.1016/j.chaos.2004.02. 035
    • (2004) Chaos Solitons Fractals , vol.22 , pp. 549-554
    • Li, C.1    Chen, G.2
  • 16
    • 34548530905 scopus 로고    scopus 로고
    • Chaotic dynamics of the fractionally damped van der Pol equation
    • DOI 10.1016/j.chaos.2006.05.010, PII S0960077906004607
    • J.H. Chen W.C. Chen 2008 Chaotic dynamics of the fractionally damped van der Pol equation Chaos Solitons Fractals 35 188 198 10.1016/j.chaos.2006.05.010 (Pubitemid 47385209)
    • (2008) Chaos, Solitons and Fractals , vol.35 , Issue.1 , pp. 188-198
    • Chen, J.-H.1    Chen, W.-C.2
  • 17
    • 33846377845 scopus 로고    scopus 로고
    • Chaos in a modified van der Pol system and in its fractional order systems
    • DOI 10.1016/j.chaos.2005.12.024, PII S0960077905012191
    • Z.M. Ge A.R. Zhang 2007 Chaos in a modified van der Pol system and in its fractional order systems Chaos Solitons Fractals 32 1791 1822 10.1016/j.chaos.2005.12.024 (Pubitemid 46136969)
    • (2007) Chaos, Solitons and Fractals , vol.32 , Issue.5 , pp. 1791-1822
    • Ge, Z.-M.1    Zhang, A.-R.2
  • 18
    • 35348886158 scopus 로고    scopus 로고
    • Chaos in the Newton-Leipnik system with fractional order
    • DOI 10.1016/j.chaos.2006.06.013, PII S096007790600587X
    • L.J. Sheu H.K. Chen J.H. Chen L.M. Tam W.C. Chen K.T. Lin Y. Kang 2008 Chaos in the Newton-Leipnik system with fractional order Chaos Solitons Fractals 36 98 103 1152.37319 10.1016/j.chaos.2006.06.013 2372049 (Pubitemid 47576640)
    • (2008) Chaos, Solitons and Fractals , vol.36 , Issue.1 , pp. 98-103
    • Sheu, L.-J.1    Chen, H.-K.2    Chen, J.-H.3    Tam, L.-M.4    Chen, W.-C.5    Lin, K.-T.6    Kang, Y.7
  • 20
    • 1542320221 scopus 로고    scopus 로고
    • Anti-control of chaos in rigid body motion
    • 1046.70005 10.1016/j.chaos.2003.12.034 2042812
    • H.K. Chen C.I. Lee 2004 Anti-control of chaos in rigid body motion Chaos Solitons Fractals 21 957 965 1046.70005 10.1016/j.chaos.2003.12.034 2042812
    • (2004) Chaos Solitons Fractals , vol.21 , pp. 957-965
    • Chen, H.K.1    Lee, C.I.2
  • 21
    • 40249084124 scopus 로고    scopus 로고
    • Parametric study of the fractional-order Chen-Lee system
    • DOI 10.1016/j.chaos.2006.09.067, PII S0960077906009295
    • L.M. Tam W.M. SiTou 2008 Parametric study of the fractional order Chen-Lee system Chaos Solitons Fractals 37 817 826 10.1016/j.chaos.2006.09.067 (Pubitemid 351335369)
    • (2008) Chaos, Solitons and Fractals , vol.37 , Issue.3 , pp. 817-826
    • Tam, L.M.1    Si Tou, W.M.2
  • 22
    • 67449116072 scopus 로고    scopus 로고
    • Alternative implementation of the chaotic Chen-Lee system
    • 10.1016/j.chaos.2008.07.053
    • L.J. Sheu L.M. Tam H.K. Chen S.K. Lao 2009 Alternative implementation of the chaotic Chen-Lee system Chaos Solitons Fractals 41 1923 1929 10.1016/j.chaos.2008.07.053
    • (2009) Chaos Solitons Fractals , vol.41 , pp. 1923-1929
    • Sheu, L.J.1    Tam, L.M.2    Chen, H.K.3    Lao, S.K.4
  • 23
    • 33748565977 scopus 로고    scopus 로고
    • Chaos in a new system with fractional order
    • DOI 10.1016/j.chaos.2005.10.073, PII S0960077905010246
    • L.J. Sheu H.K. Chen J.H. Chen L.M. Tam 2007 Chaos in a new system with fractional order Chaos Solitons Fractals 31 1203 1212 10.1016/j.chaos.2005.10. 073 (Pubitemid 44363163)
    • (2007) Chaos, Solitons and Fractals , vol.31 , Issue.5 , pp. 1203-1212
    • Sheu, L.-J.1    Chen, H.-K.2    Chen, J.-H.3    Tam, L.-M.4
  • 24
    • 0002731965 scopus 로고    scopus 로고
    • Stability results of fractional differential equations with applications to control processing
    • France
    • Matignon, D.: Stability results of fractional differential equations with applications to control processing. In: Proceedings of IMACS, IEEE-SMC, pp. 963-968. France (1996)
    • (1996) Proceedings of IMACS, IEEE-SMC , pp. 963-968
    • Matignon, D.1
  • 25
    • 33947133956 scopus 로고    scopus 로고
    • Stability analysis of linear fractional differential system with multiple time delays
    • DOI 10.1007/s11071-006-9094-0
    • W. Deng C. Li J. Lü 2007 Stability analysis of linear fractional differential system with multiple time delays Nonlinear Dyn. 48 409 416 1185.34115 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
  • 26
    • 33750295344 scopus 로고    scopus 로고
    • Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models
    • DOI 10.1016/j.jmaa.2006.01.087, PII S0022247X06000801
    • E. Ahmed A. El-Sayed H. El-Saka 2007 Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models J. Math. Anal. Appl. 325 542 553 1105.65122 10.1016/j.jmaa.2006.01.087 2273544 (Pubitemid 44615337)
    • (2007) Journal of Mathematical Analysis and Applications , vol.325 , Issue.1 , pp. 542-553
    • Ahmed, E.1    El-Sayed, A.M.A.2    El-Saka, H.A.A.3
  • 27
    • 51249088596 scopus 로고    scopus 로고
    • Chaotic attractors in incommensurate fractional order systems
    • 1157.26310 10.1016/j.physd.2008.03.037 2514122
    • M.S. Tavazoei M. Haeri 2008 Chaotic attractors in incommensurate fractional order systems Physica D 237 2628 2637 1157.26310 10.1016/j.physd. 2008.03.037 2514122
    • (2008) Physica D , vol.237 , pp. 2628-2637
    • Tavazoei, M.S.1    Haeri, M.2
  • 28
    • 34347330038 scopus 로고    scopus 로고
    • A necessary condition for double scroll attractor existence in fractional-order systems
    • 10.1016/j.physleta.2007.05.081
    • M.S. Tavazoei M. Haeri 2007 A necessary condition for double scroll attractor existence in fractional-order systems Phys. Lett. A 367 102 113 10.1016/j.physleta.2007.05.081
    • (2007) Phys. Lett. A , vol.367 , pp. 102-113
    • Tavazoei, M.S.1    Haeri, M.2
  • 30
    • 0001618393 scopus 로고    scopus 로고
    • An algorithm for the numerical solution of differential equations of fractional order
    • K. Diethelm 1997 An algorithm for the numerical solution of differential equations of fractional order Electron. Trans. Numer. Anal. 5 1 6 0890.65071 1447831 (Pubitemid 38870919)
    • (1997) Electronic Transactions on Numerical Analysis , vol.5 , pp. 1-6
    • Diethelm, K.1
  • 31
    • 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
    • K. Diethelm N.J. Ford A.D. Freed 2002 A predictor-corrector approach for the numerical solution of fractional differential equations Nonlinear Dyn. 29 3 22 1009.65049 10.1023/A:1016592219341 1926466 (Pubitemid 34945390)
    • (2002) Nonlinear Dynamics , vol.29 , Issue.1-4 , pp. 3-22
    • Diethelm, K.1    Ford, N.J.2    Freed, A.D.3
  • 32
    • 0026928376 scopus 로고
    • Fractal system as represented by singularity function
    • DOI 10.1109/9.159595
    • A. Charef H.H. Sun Y.Y. Tsao B. Onaral 1992 Fractal system as represented by singularity function IEEE Trans. Autom. Control 37 1465 1470 0825.58027 10.1109/9.159595 1183117 (Pubitemid 23555835)
    • (1992) IEEE Transactions on Automatic Control , vol.37 , Issue.9 , pp. 1465-1470
    • Charef, A.1    Sun, H.H.2    Tsao, Y.Y.3    Onaral, B.4
  • 33
    • 37549042003 scopus 로고    scopus 로고
    • Unreliability of frequency-domain approximation in recognizing chaos in fractional-order systems
    • 10.1049/iet-spr:20070053
    • M.S. Tavazoei M. Haeri 2007 Unreliability of frequency-domain approximation in recognizing chaos in fractional-order systems IET Signal Process. 1 171 181 10.1049/iet-spr:20070053
    • (2007) IET Signal Process. , vol.1 , pp. 171-181
    • Tavazoei, M.S.1    Haeri, M.2
  • 34
    • 18444371474 scopus 로고    scopus 로고
    • Synchronization of two different chaotic systems: A new system and each of the dynamical systems Lorenz, Chen and Lü
    • DOI 10.1016/j.chaos.2004.11.032, PII S0960077904007829
    • H.K. Chen 2005 Synchronization of two different chaotic systems: a new system and each of the dynamical systems Lorenz, Chen and Lü Chaos Solitons Fractals 25 1049 1056 02191087 10.1016/j.chaos.2004.11.032 2144653 (Pubitemid 40643057)
    • (2005) Chaos, Solitons and Fractals , vol.25 , Issue.5 , pp. 1049-1056
    • Chen, H.-K.1
  • 35
    • 22844452048 scopus 로고    scopus 로고
    • Chaos synchronization between two different chaotic dynamical systems
    • DOI 10.1016/j.chaos.2005.03.049, PII S0960077905003553
    • J.H. Park 2006 Chaos synchronization between two different chaotic dynamical systems Chaos Solitons Fractals 27 549 554 1102.37304 10.1016/j.chaos.2005.03.049 (Pubitemid 41037139)
    • (2006) Chaos, Solitons and Fractals , vol.27 , Issue.2 , pp. 549-554
    • Park, J.H.1
  • 36
    • 62749097343 scopus 로고    scopus 로고
    • Synchronization and anti-synchronization coexist in Chen-Lee chaotic systems
    • 10.1016/j.chaos.2007.01.104
    • J.H. Chen H.K. Chen Y.K. Lin 2009 Synchronization and anti-synchronization coexist in Chen-Lee chaotic systems Chaos Solitons Fractals 39 707 716 10.1016/j.chaos.2007.01.104
    • (2009) Chaos Solitons Fractals , vol.39 , pp. 707-716
    • Chen, J.H.1    Chen, H.K.2    Lin, Y.K.3
  • 37
    • 0008494528 scopus 로고
    • Determining Lyapunov exponents from a time series
    • 0585.58037 10.1016/0167-2789(85)90011-9 805706
    • A. Wolf J.B. Swift H.L. Swinney J.A. Vastano 1985 Determining Lyapunov exponents from a time series Physica D 16 285 317 0585.58037 10.1016/0167-2789(85)90011-9 805706
    • (1985) Physica D , vol.16 , pp. 285-317
    • Wolf, A.1    Swift, J.B.2    Swinney, H.L.3    Vastano, J.A.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.