Constructing generalized synchronization manifolds by manifold equation

SIAM Journal on Applied Dynamical Systems

Volumn 8, Issue 1, 2009, Pages 202-221

  Jie, Sun ^a   Bollt, Erik M ^a   Nishikawa, Takashi ^a  

^a CLARKSON UNIVERSITY   (United States)

Author keywords

Computational invariant manifold; Coupled dynamical systems; Generalized synchronization

Indexed keywords

COMPUTATIONAL INVARIANT MANIFOLD; COUPLED DYNAMICAL SYSTEMS; EXPLICIT CONSTRUCTIONS; FIRST ORDERS; GENERALIZED SYNCHRONIZATION; IDENTITY FUNCTIONS; NOVEL METHODS; NUMERICAL SCHEMES; STATIONARY SOLUTIONS; TIME DEPENDENT PDES; VAN DER POL OSCILLATORS;

AIRCRAFT ENGINES; CIRCUIT OSCILLATIONS; NONLINEAR CONTROL SYSTEMS; SYNCHRONIZATION; SYSTEM STABILITY;

DYNAMICAL SYSTEMS;

EID: 63049095636     PISSN: None     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/080721340     Document Type: Article

References (20)

1. J. CARR, Applications of Centre Manifold Theory, Springer, New York, 1981.
2. L. M. PÉ;CORA AND T. L. CARROLL, Synchronization in chaotic systems, Phys. Rev. Lett., 64 (1990), pp. 821-824.
3. N. F. RULKOV, M. M. SUSHCHIK, AND L. S. TSIMRING, Generalized synchronization of chaos in directionally coupled chaotic systems, Phys. Rev. E, 51 (1995), pp. 980-994.
4. H. D. I. ABARBANEL, N. F. RULKOV, AND M. M. SUSHCHIK, Generalized synchronization of chaos: The auxiliary system approach, Phys. Rev. E, 53 (1996), pp. 4528-4535.
5. M. G. ROSENBLUM, A. S. PIKOVSKY, AND J. KURTHS, Phase synchronization of chaotic oscillators, Phys. Rev. Lett., 76 (1996), pp. 1804-1807.
6. L. KOCAREV AND U. PARLITZ, Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems, Phys. Rev. Lett., 76 (1996), pp. 1816-1819.
7. K. T. ALLIGOOD, T. D. SAUER, AND J. A. YORKE, Chaos, Springer, New York, 1997.
8. M. G. ROSENBLUM, A. S. PIKOVSKY, AND J. KURTHS, From phase to lag synchronization in coupled chaotic oscillators, Phys. Rev. Lett., 78 (1997), pp. 4193-4196.
9. R. BROWN AND N. F. RULKOV, Synchronization of chaotic systems: Transverse stability of trajectories in invariant manifolds, Chaos, 7 (1997), pp. 395-413.
10. M. DING, E.-J. DING, W. L. DITTO, B. GLUCKMAN, V. IN, J.-H. PENG, M. L. SPANO, AND W. YANG, Control and synchronization of chaos in high dimensional systems: Review of some recent results, Chaos, 7 (1997), pp. 644-652.
11. L. M. PÉ;CORA AND T. L. CARROLL, Master stability functions for synchronized coupled systems, Phys. Rev. Lett., 80 (1998), pp. 2109-2112.
12. K. JOSIĆ, Invariant manifolds and synchronization of coupled dynamical systems, Phys. Rev. Lett., 80 (1998), pp. 3053-3056.
13. R. BROWN, Approximating the mapping between systems exhibiting generalized synchronization, Phys. Rev. Lett., 81 (1998), pp. 4835-4838.
14. K. JOSIĆ, Synchronization of chaotic systems and invariant manifolds, Nonlinearity, 13 (2000), pp. 1321-1336.
15. C. MASOLLER, Anticipation in the synchronization of chaotic semiconductor lasers with optical feedback, Phys. Rev. Lett., 86 (2001), pp. 2782-2785.
16. J. CHUBB, E. BARRETO, P. SO, AND B. J. GLUCKMAN, The breakdown of synchronization in systems of nonidentical chaotic oscillators: Theory and experiment, Internat. J. Bif. Chaos Appl. Sei. Engrg., 11 (2001), pp. 2705-2713.
17. E. OTT, Chaos in Dynamical Systems, 2nd ed., Cambridge University Press, Cambridge, UK, 2002.
18. A. UCHIDA, R. MCALLISTER, R. MEUCCI, AND R. ROY, Generalized synchronization of chaos in identical systems with hidden degrees of freedom, Phys. Rev. Lett., 91 (2003), paper 174101.
19. A. ARENAS, A. DÍAZ-GUILERA, AND C. J. PÉ;REZ-VICENTE, Synchronization reveals topological scales in complex networks, Phys. Rev. Lett., 96 (2006), paper 114102.
20. F. SORRENTINO AND E. OTT, Network synchronization of groups, Phys. Rev. E, 76 (2007), paper 056114.