Heteroclinic cycles between unstable attractors

Nonlinearity

Volumn 21, Issue 6, 2008, Pages 1385-1410

  Broer, Henk ^a   Efstathiou, Konstantinos ^a   Subramanian, Easwar ^a  

^a UNIVERSITY OF GRONINGEN   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 44949249817     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/21/6/014     Document Type: Article

References (28)

1. Krupa M 1997 Robust heteroclinic cycles J. Nonlinear Sci. 7 129-76
2. Guckenheimer J and Holmes P 1988 Structurally stable heteroclinic cycles Math. Proc. Camb. Phil. Soc. 103 189-92
3. Busse F M and Heikes K E 1980 Convection in a rotating layer: a simple case of turbulence Science 208 173-5
4. May R M and Leonard W 1975 Nonlinear aspects of competition between three species SIAM J. Appl. Math. 29 243-52
5. Stewart I 2003 Mathematics: regime change in meterology Nature 422 571-3
6. Timme M, Wolf F and Geisel T 2002 Unstable attractors induce perpetual synchronization and desynchronization Chaos 13 377-87
7. Ashwin P and Borresen J 2005 Discrete computation using a perturbed heteroclinic network Phys. Lett. A 347 208-14
8. Mirollo R and Strogatz S H 1990 Synchronization of pulse-coupled biological oscillators SIAM J. Appl. Math. 50 1645-62
9. Wu W and Chen T 2007 Desynchronization of pulse-coupled oscillators with delayed excitatory coupling Nonlinearity 20 789-808
10. Ernst U, Pawelzik K and Geisel T 1995 Synchronization induced by temporal delays in pulse-coupled oscillators Phys. Rev. Lett. 74 1570-3
11. Timme M, Wolf F and Geisel T 2002 Prevalence of unstable attractors in networks of pulse-coupled oscillators Phys. Rev. Lett. 89 154105
12. Ashwin P and Timme M 2005 Unstable attractors: existence and robustness in networks of oscillators with delayed pulse coupling Nonlinearity 18 2035-60
13. Rabinovich M, Volkovskii A, Lecanda P, Huerta R, Abarbanel H D I and Laurent G 2001 Dynamical encoding by networks of competing neuron groups: winnerless competition Phys. Rev. Lett. 87 068102
14. Huerta R, Nowotny T, Garca-Sanchez M, Abarbanel H and Rabinovich M I 2004 Learning classification in the olfactory system of insects Neural Comput. 16 1601-40
15. Huerta R and Rabinovich M 2004 Reproducible sequence generation in random neural ensembles Phys. Rev. Lett. 93 238104
16. Hansel D, Mato G and Meunier C 1993 Clustering and slow switching in globally coupled phase oscillators Phys. Rev. E 48 3470-7
17. Kori H and Kuramoto Y 2001 Slow switching in globally coupled oscillators: robustness and occurrence through delayed coupling Phys. Rev. E 63 046214
18. Ashwin P and Timme M 2005 When instablity makes sense Nature 436 36-7
19. Broer H W, Efstathiou K and Subramanian V E 2005 Robustness of unstable attractors in arbitrarily sized pulse-coupled systems with delay Nonlinearity 21 13-49
20. Diekmann O, van Gills S A, Verduyn Lunel S M and Walther H-O 1995 Delay Equations: Functional-, Complex-, and Nonlinear Analysis (Berlin: Springer)
21. Katok A and Hasselblatt B 1995 Introduction to the Modern Theory of Dynamical Systems (Cambridge, UK: Cambridge University Press)
22. Broer H W and Takens F 2008 Dynamical Systems and Chaos (Epsilon Uitgaven) at press
23. Strogatz S H 1994 Nonlinear Dynamics and Chaos (Reading, MA: Addison Wesley)
24. Rabinovich M, Varona P, Selverston A I and Abarbanel H D I 2006 Dynamical principles in neuroscience Rev. Mod. Phys. 78 1213-65
25. Zumdieck A, Timme M, Geisel T and Wolf F 2004 Long chaotic transients in complex networks Phys. Rev. Lett. 93 244103
26. Watts D and Strogatz S 1998 Collective dynamics of 'small-world' networks Nature 393 440-4
27. Raghavachari S and Glazier J 1995 Spatially coherent states in fractally coupled map lattices Phys. Rev. Lett. 74 3297-300
28. Raghavachari S 1999 Synchrony and chaos in coupled oscillators and neural networks PhD Thesis University of Notre Dame