메뉴 건너뛰기




Volumn 13, Issue 2, 2012, Pages 779-789

A note on phase synchronization in coupled chaotic fractional order systems

Author keywords

Caputo fractional derivative; Chaos; Control; Fractional order system; L system; Lorenz system; Phase synchronization; R ssler system; Stability; Synchronization

Indexed keywords

CAPUTO FRACTIONAL DERIVATIVES; FRACTIONAL-ORDER SYSTEMS; L-SYSTEMS; LORENZ SYSTEM; PHASE SYNCHRONIZATION;

EID: 80054903851     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2011.08.016     Document Type: Article
Times cited : (95)

References (48)
  • 2
    • 0000796972 scopus 로고
    • Stability theory of synchronized motion in coupled-oscillator systems
    • T. Yamada, and H. Fujisaka Stability theory of synchronized motion in coupled-oscillator systems Progr. Theoret. Phys. 70 1983 1240 1248
    • (1983) Progr. Theoret. Phys. , vol.70 , pp. 1240-1248
    • Yamada, T.1    Fujisaka, H.2
  • 3
    • 0343689904 scopus 로고
    • Synchronization in chaotic systems
    • L.M. Pecora, and T.L. Carrol Synchronization in chaotic systems Phys. Rev. Lett. 64 1990 821 824
    • (1990) Phys. Rev. Lett. , vol.64 , pp. 821-824
    • Pecora, L.M.1    Carrol, T.L.2
  • 7
    • 0000929946 scopus 로고    scopus 로고
    • Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems
    • L. Kocarev, and U. Parlitz Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems Phys. Rev. E 76 11 1996 1816 1819 (Pubitemid 126638874)
    • (1996) Physical Review Letters , vol.76 , Issue.11 , pp. 1816-1819
    • Kocarev, L.1    Parlitz, U.2
  • 8
    • 0031548743 scopus 로고    scopus 로고
    • From phase to Lag synchronization in coupled chaotic oscillators
    • M.G. Rosenblum, A.S. Pikovsky, and J. Kurths From phase to Lag synchronization in coupled chaotic oscillators Phys. Rev. Lett. 78 22 1996 4193 4196
    • (1996) Phys. Rev. Lett. , vol.78 , Issue.22 , pp. 4193-4196
    • Rosenblum, M.G.1    Pikovsky, A.S.2    Kurths, J.3
  • 9
    • 0033197402 scopus 로고    scopus 로고
    • Synchronization and control of chaotic systems
    • E. Bai, and K. Lonngren Synchronization and control of chaotic systems Chaos Solitons Fractals 10 9 1999 1571 1575
    • (1999) Chaos Solitons Fractals , vol.10 , Issue.9 , pp. 1571-1575
    • Bai, E.1    Lonngren, K.2
  • 10
    • 0034637788 scopus 로고    scopus 로고
    • Anti-phase synchronization in coupled map lattices
    • J. Liu, C. Ye, S. Zhang, and W. Song Anti-phase synchronization in coupled map lattices Phys. Lett. A 274 12 2000 27 29
    • (2000) Phys. Lett. A , vol.274 , Issue.12 , pp. 27-29
    • Liu, J.1    Ye, C.2    Zhang, S.3    Song, W.4
  • 11
    • 0037041689 scopus 로고    scopus 로고
    • Phase and anti-phase synchronization of two chaotic systems by using active control
    • M. Ho, Y. Hung, and C. Chou Phase and anti-phase synchronization of two chaotic systems by using active control Phys. Lett. A 296 1 2002 43 48
    • (2002) Phys. Lett. A , vol.296 , Issue.1 , pp. 43-48
    • Ho, M.1    Hung, Y.2    Chou, C.3
  • 12
    • 41849104190 scopus 로고    scopus 로고
    • A note on the fractional-order Chua's system
    • DOI 10.1016/j.chaos.2006.10.054, PII S0960077906010290
    • I. Petrá A note on the fractional-order Chua's system Chaos Solitons Fractals 38 1 2008 140 147 (Pubitemid 351503975)
    • (2008) Chaos, Solitons and Fractals , vol.38 , Issue.1 , pp. 140-147
    • Petras, I.1
  • 13
    • 34147144036 scopus 로고    scopus 로고
    • Chaos in a fractional order modified duffing system
    • Z.M. Ge, and C.Y. Ou Chaos in a fractional order modified duffing system Chaos Solitons Fractals 34 2 2007 262 291
    • (2007) Chaos Solitons Fractals , vol.34 , Issue.2 , pp. 262-291
    • Ge, Z.M.1    Ou, C.Y.2
  • 15
    • 3342927052 scopus 로고    scopus 로고
    • Chaos and hyperchaos in fractional order Rössler equations
    • C. Li, and G. Chen Chaos and hyperchaos in fractional order Rössler equations Physica A 341 2004 55 61
    • (2004) Physica A , vol.341 , pp. 55-61
    • Li, C.1    Chen, G.2
  • 16
    • 2042470796 scopus 로고    scopus 로고
    • Chaos in the fractional order Chen system and its control
    • C. Li, and G. Chen Chaos in the fractional order Chen system and its control Chaos Solitons Fractals 22 3 2004 549 554
    • (2004) Chaos Solitons Fractals , vol.22 , Issue.3 , pp. 549-554
    • Li, C.1    Chen, G.2
  • 17
    • 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. L, and G. Chen A note on the fractional-order Chen system Chaos Solitons Fractals 27 3 2006 685 688 (Pubitemid 41084201)
    • (2006) Chaos, Solitons and Fractals , vol.27 , Issue.3 , pp. 685-688
    • Lu, J.G.1    Chen, G.2
  • 18
    • 0041384356 scopus 로고    scopus 로고
    • Chaotic dynamics of the fractional Lorenz system
    • I. Grigorenko, and E. Grigorenko Chaotic dynamics of the fractional Lorenz system Phys. Rev. Lett. 91 3 2003 034101
    • (2003) Phys. Rev. Lett. , vol.91 , Issue.3 , pp. 034101
    • Grigorenko, I.1    Grigorenko, E.2
  • 20
    • 18844427587 scopus 로고    scopus 로고
    • Chaos synchronization of the fractional L system
    • W.H. Deng, and C.P. Li Chaos synchronization of the fractional L system Physica A 353 2005 61 72
    • (2005) Physica A , vol.353 , pp. 61-72
    • Deng, W.H.1    Li, C.P.2
  • 21
    • 27744462122 scopus 로고    scopus 로고
    • Synchronization in fractional-order differential systems
    • DOI 10.1016/j.physd.2005.09.012, PII S0167278905004070
    • C. Li, and T. Zhou Synchronization in fractional-order differential systems Physica D 212 12 2005 111 125 (Pubitemid 41617927)
    • (2005) Physica D: Nonlinear Phenomena , vol.212 , Issue.1-2 , pp. 111-125
    • Zhou, T.1    Li, C.2
  • 22
    • 38349181868 scopus 로고    scopus 로고
    • Chaos control and synchronization in a fractional neuron network system
    • S. Zhou, H. Li, and Z. Zhu Chaos control and synchronization in a fractional neuron network system Chaos Solitons Fractals 36 4 2008 973 984
    • (2008) Chaos Solitons Fractals , vol.36 , Issue.4 , pp. 973-984
    • Zhou, S.1    Li, H.2    Zhu, Z.3
  • 23
    • 33847065079 scopus 로고    scopus 로고
    • Synchronization of fractional order chaotic systems
    • G. Peng Synchronization of fractional order chaotic systems Phys. Lett. A 363 56 2007 426 432
    • (2007) Phys. Lett. A , vol.363 , Issue.56 , pp. 426-432
    • Peng, G.1
  • 25
    • 33749563875 scopus 로고    scopus 로고
    • On chaos synchronization of fractional differential equations
    • DOI 10.1016/j.chaos.2005.11.062, PII S0960077905011069
    • J. Yan, and C. Li On chaos synchronization of fractional differential equations Chaos Solitons Fractals 32 2 2007 725 735 (Pubitemid 44537762)
    • (2007) Chaos, Solitons and Fractals , vol.32 , Issue.2 , pp. 725-735
    • Yan, J.1    Li, C.2
  • 26
    • 33749553588 scopus 로고    scopus 로고
    • The synchronization of three fractional differential systems
    • DOI 10.1016/j.chaos.2005.11.020, PII S0960077905011100
    • C. Li, and J. Yan The synchronization of three fractional differential systems Chaos Solitons Fractals 32 2 2007 751 757 (Pubitemid 44537765)
    • (2007) Chaos, Solitons and Fractals , vol.32 , Issue.2 , pp. 751-757
    • Li, C.1    Yan, J.2
  • 27
    • 33748178408 scopus 로고    scopus 로고
    • Extending synchronization scheme to chaotic fractional-order Chen systems
    • DOI 10.1016/j.physa.2006.03.021, PII S0378437106003530
    • J. Wang, X. Xiong, and Y. Zhang Extending synchronization scheme to chaotic fractional-order Chen systems Physica A 370 2 2006 279 285 (Pubitemid 44310881)
    • (2006) Physica A: Statistical Mechanics and its Applications , vol.370 , Issue.2 , pp. 279-285
    • Wang, J.1    Xiong, X.2    Zhang, Y.3
  • 28
    • 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, and D. Xu Chaos synchronization of the Chua system with a fractional order Physica A 360 2 2006 171 185 (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
  • 29
    • 63449132495 scopus 로고    scopus 로고
    • Chaos and synchronization of the fractional-order Chua's system
    • H. Zhu, S. Zhou, and J. Zhang Chaos and synchronization of the fractional-order Chua's system Chaos Solitons Fractals 39 4 2009 1595 1603
    • (2009) Chaos Solitons Fractals , vol.39 , Issue.4 , pp. 1595-1603
    • Zhu, H.1    Zhou, S.2    Zhang, J.3
  • 30
    • 77956595176 scopus 로고    scopus 로고
    • A new chaotic system with fractional order and its projective synchronization
    • X. Wu, and H. Wang A new chaotic system with fractional order and its projective synchronization Nonlinear Dynam. 61 3 2010 407 417
    • (2010) Nonlinear Dynam. , vol.61 , Issue.3 , pp. 407-417
    • Wu, X.1    Wang, H.2
  • 31
    • 77955654277 scopus 로고    scopus 로고
    • Adaptive feedback control and synchronization of non-identical chaotic fractional order systems
    • Z. Odibat Adaptive feedback control and synchronization of non-identical chaotic fractional order systems Nonlinear Dynam. 60 4 2010 479 487
    • (2010) Nonlinear Dynam. , vol.60 , Issue.4 , pp. 479-487
    • Odibat, Z.1
  • 33
    • 37349129071 scopus 로고    scopus 로고
    • Phase and lag synchronization in coupled fractional order chaotic oscillators
    • C. Li Phase and lag synchronization in coupled fractional order chaotic oscillators Internat. J. Modern Phys. B 21 30 2007 5159 5166
    • (2007) Internat. J. Modern Phys. B , vol.21 , Issue.30 , pp. 5159-5166
    • Li, C.1
  • 34
    • 40249087307 scopus 로고    scopus 로고
    • Phase synchronization in fractional differential chaotic systems
    • G.H. Erjaee, and S. Momani Phase synchronization in fractional differential chaotic systems Phys. Lett. A 372 14 2008 2350 2354
    • (2008) Phys. Lett. A , vol.372 , Issue.14 , pp. 2350-2354
    • Erjaee, G.H.1    Momani, S.2
  • 38
    • 77954268265 scopus 로고    scopus 로고
    • Fractional calculus: Integral and differential equations of fractional order
    • Carpinteri and Mainardi (Ed.) New York
    • R. Gorenflo, F. Mainardi, Fractional calculus: integral and differential equations of fractional order, in: Carpinteri and Mainardi (Ed.), Fractals and Fractional Calculus, New York, 1997.
    • (1997) Fractals and Fractional Calculus
    • Gorenflo, R.1    Mainardi, F.2
  • 39
    • 84977255207 scopus 로고
    • Linear models of dissipation whose Q is almost frequency independent, part II
    • M. Caputo Linear models of dissipation whose Q is almost frequency independent, part II J. R. Astron. Soc. 13 1967 529 539
    • (1967) J. R. Astron. Soc. , vol.13 , pp. 529-539
    • Caputo, M.1
  • 40
    • 0002731965 scopus 로고    scopus 로고
    • Stability results of fractional differential equations with applications to control processing
    • IEEE-SMC, Lille, France
    • D. Matignon, Stability results of fractional differential equations with applications to control processing, in: Proceeding of IMACS, IEEE-SMC, Lille, France, 1996, pp. 963968.
    • (1996) Proceeding of IMACS , pp. 963-968
    • Matignon, D.1
  • 41
    • 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, and J. L Stability analysis of linear fractional differential system with multiple time delays Nonlinear Dynam. 48 2007 409 416 (Pubitemid 46407957)
    • (2007) Nonlinear Dynamics , vol.48 , Issue.4 , pp. 409-416
    • Deng, W.1    Li, C.2    Lu, J.3
  • 42
    • 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.M. El-Sayed, and H. El-Saka Equilibrium points, stability and numerical solutions of fractional-order predatorprey and rabies models J. Math. Anal. Appl. 325 1 2007 542 553 (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
  • 43
    • 57649105528 scopus 로고    scopus 로고
    • A note on the stability of fractional order systems
    • M.S. Tavazoei, and M. Haeri A note on the stability of fractional order systems Math. Comput. Simulation 79 5 2009 1566 1576
    • (2009) Math. Comput. Simulation , vol.79 , Issue.5 , pp. 1566-1576
    • Tavazoei, M.S.1    Haeri, M.2
  • 44
    • 0000241853 scopus 로고
    • Deterministic nonperiodic flow
    • E. Lorenz Deterministic nonperiodic flow J. Atmos. Sci. 20 1963 130 141
    • (1963) J. Atmos. Sci. , vol.20 , pp. 130-141
    • Lorenz, E.1
  • 45
    • 51249088596 scopus 로고    scopus 로고
    • Chaotic attractors in incommensurate fractional order systems
    • M.S. Tavazoei, and M. Haeri Chaotic attractors in incommensurate fractional order systems Physica D 237 2008 2628 2637
    • (2008) Physica D , vol.237 , pp. 2628-2637
    • Tavazoei, M.S.1    Haeri, M.2
  • 47
    • 0037332676 scopus 로고    scopus 로고
    • Controlling uncertain Lü system using backstepping design
    • DOI 10.1016/S0960-0779(02)00205-9, PII S0960077902002059
    • Y. Yongguang, and Z. Suochun Controlling uncertain L system using backstepping design Chaos Solitons Fractals 15 5 2003 897 902 (Pubitemid 35152326)
    • (2003) Chaos, Solitons and Fractals , vol.15 , Issue.5 , pp. 897-902
    • Yongguang, Y.1    Suochun, Z.2
  • 48
    • 49549126801 scopus 로고
    • An equation for continuous chaos
    • O.E. Rossler An equation for continuous chaos Phys. Lett. A 57 5 1976 397 398
    • (1976) Phys. Lett. A , vol.57 , Issue.5 , pp. 397-398
    • Rossler, O.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.