Synchronization of chaotic systems and invariant manifolds

Nonlinearity

Volumn 13, Issue 4, 2000, Pages 1321-1336

  Josić, Kreŝimir ^a  

^a USA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034215357     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/13/4/318     Document Type: Article

References (44)

1. Afraimovich V S, Verichev N N and Rabinovich MI 1986 Stochastic synchronization of oscillations in dissipative systems Radio Phys. Quantum Electron. 29 747-51
2. Fujisaka H and Yamada T 1983 Stability theory of synchronized motion in coupled oscillator systems Prog. Theor. Phys. 69 32-47
3. Pecora L M and Carroll T L 1990 Synchronization in chaotic systems Phys. Rev. Lett. 64 821-4
4. Abarbanel H D I, Rulkov N F and Sushchik M 1996 Generalized synchronization of chaos: the auxiliary approach Phys. Rev. E 53 4528-35
5. Kocarev L and Parlitz U 1996 Generalized synchronization, predictability and equivalence of unidirectionally coupled dynamical systems Phys. Rev. Lett. 76 1816-9
6. Hale J 1997 Diffusive coupling, dissipation and synchronization J. Dyn. Differ. Equ. 9 1-52
7. Rosenblum M G, Pikovsky A S and Kurths J 1996 Phase synchronization of chaotic oscillators Phys. Rev. Lett. 76 1804-7
8. Chua L O and Itoh M 1993 Chaos synchronization in Chua's circuit J. Circuits Syst. Comput. 3 93-108
9. Alsing P M, Gavrielides A, Kovanis V, Roy R and Thornburg K S 1997 Encoding and decoding messages with chaot c lasers Phys. Rev. E 56 6302-10
10. Mirollo R E and Strogatz S H 1990 Synchronization of pulse-coupled biological oscillators SIAM J. Appl. Math. 50 1645-62
11. Watanabe S, van der Zant H S J, Strogatz S H and Orlando T P 1996 Dynamics of circular arrays of Josephson junctions and the discrete sine-Gordon equation Physica D 97 429-70
12. Maybhate A and Amritkar R E 1999 Use of synchronization and adaptive control in parameter estimation from a time series Phys. Rev. E 59 284-93
13. Pyragas K 1992 Continuous control of chaos by self-controlling feedback Phys. Lett. A 170 421-8
14. Pyragas K 1993 Predictable chaos in slightly perturbed unpredictable chaotic systems Phys. Lett. A 181 203-10
15. Zanette D H and Mikhailov A S 1998 Condensation in globally copuled populations of chaotic dynamical systems Phys. Rev. E 57 276-81
16. Pecora L M et al 1997 Fundamentals of synchronization in chaotic systems, concepts and applications Chaos 7 520-43
17. Rulkov N F 1996 Images of synchronized chaos: experiments with circuits Chaos 6 262-78
18. Bronstein I U and Kopanskii A Ya 1994 Smooth Invariant Manifolds and Normal Forms (Singapore: World Scientific)
19. Wiggins S 1994 Normally Hyperbolic Invariant Manifolds in Dynamical Systems (Berlin: Springer)
20. Spivak M 1979 A Comprehensive Introduction to Differential Geometry (Boston, MA: Publish or Perish)
21. Fenichel N 1971 Persistence and smoothness of invariant manifolds for flows Ind. Univ. Math. J. 21 193-226
22. Abraham R, Marsden J E and Ratiu T 1983 Manifolds, Tensor Analysis and Applications (Reading, MA: Addison-Wesley)
23. Chow S-N and Liu W 1997 Synchronization, stability and normal hyperbolicity Resenhas IME-USP 3 139-58
24. Josić K 1998 Invariant manifolds and synchronization of coupled dynamical systems Phys. Rev. Lett. 80 3053-7
25. Josić K 1999 Synchronization of chaotic systems Thesis Pennsylvania State University
26. Ashwin P, Buescu J and Stewart I 1996 From attractor to chaotic saddle: a tale of transverse instability Nonlinearity 9 703-37
27. Ashwin P, Buescu J and Stewart I 1994 Bubbling of attractors and synchronisation of chaotic oscillators Phys. Lett. A 193 126-39
28. Gauthier D and Bienfang J 1996 Intermittent loss of synchronization in coupled chaotic oscillators: toward a new criterion for high-quality synchronization Phys. Rev. Lett. 77 1751-4
29. Hunt B and Ott E 1996 Optimal periodic orbits of chaotic systems occur at low period Phys. Rev. E 54 328-37
30. Hunt B and Yuan G Optimal orbits of hyperbolic systems Preprint
31. Hale J 1959 Ordinary Differential Equations (New York: Krieger)
32. Hadjiloucas D, Nicolas M J and Walkden C P Regularity of invariant graphs over hyperbolic systems Preprint
33. Stark J 1997 Invariant graphs for forced systems Physica D 109 163-79
34. Stark J 1999 Regularity of invariant graphs for forced systems Ergod. Theor. Dynam. Syst. 19 155-99
35. Hunt B, Ott E and Yorke J 1997 Differentiable generalized synchronization of chaos Phys. Rev. E 55 4029-34
36. 2 Preprint
37. Hirsch M W, Pugh C C and Shub M 1977 Invariant Manifolds (Lecture Notes in Mathematics vol 583) (Berlin: Springer)
38. Bronštein I U 1979 Extensions of Minimal Transformation Groups (Groningen: Sijthoff and Noordhoff)
39. Bronshteyn I U Private communication
40. Parlitz U, Junge L and Kocarev Lj 1997 Subharmonic entrainment of unstable periodic orbits and generalized synchronization Phys. Rev. Lett. 79 3158-61
41. Afraimovich V S 1999 Poincaré recurrences of coupled subsystems in synchronized regimes Taiwanese J. Math. 3 139-61
42. Afraimovich V S and Zaslavsky G M 1997 Fractal and multifractal properties of exit times and Poincaré recurrences Phys. Rev. E 55 5418-26
43. Jones C K R T 1994 Geometric Singular Perturbation Theory (Lecture Notes in Mathematics vol 1609) pp 44-118
44. Barreto E, So P, Gluckman B J and Schiff S J 2000 From generalized synchrony to topological decoherence: emergent sets in coupled chaotic systems Phys. Rev. Lett. 84 1689-92