On the occurrence of stable heteroclinic channels in Lotka-Volterra models

Dynamical Systems

Volumn 25, Issue 1, 2010, Pages 97-110

  Bick, Christian ^a,b   Rabinovich, Mikhail I ^b  

^a UNIVERSITY OF CALIFORNIA SAN DIEGO   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Dynamical systems; Lotka Volterra model; Neural computation; Random networks; Spatio temporal coding; Transient dynamics

Indexed keywords

LOTKA-VOLTERRA MODELS; NEURAL COMPUTATIONS; RANDOM NETWORK; SPATIO-TEMPORAL; TRANSIENT DYNAMICS;

DYNAMICAL SYSTEMS; NEURAL NETWORKS;

MATHEMATICAL MODELS;

EID: 77949594943     PISSN: 14689367     EISSN: 14689375     Source Type: Journal    
DOI: 10.1080/14689360903322227     Document Type: Article

References (20)

1. M. Abeles, H. Bergman, I. Gat, I. Meilijson, E. Seidemann, N. Tishby, and E. Vaadia, Cortical activity flips among quasi-stationary states, Proc. Natl. Acad. Sci. USA 92 (1995), pp. 8616-8620.
2. P. Ashwin and M. Timme, Nonlinear dynamics: When instability makes sense, Nature 436 (2005), pp. 36-37.
3. M.I. Rabinovich, A. Volkovskii, P. Lecanda, R. Huerta, H.D.I. Abarbanel, and G. Laurent, Dynamical encoding by networks of competing neuron groups: Winnerless competition, Phys. Rev. Lett. 87 (2001), p. 068102.
4. A.A. Fingelkurts and A.A. Fingelkurts, Timing in cognition and EEG brain dynamics: Discreteness versus continuity, Cogn. Process. 7 (2006), pp. 135-162.
5. K.J. Friston, Transients, metastability, and neuronal dynamics, NeuroImage 5 (1997), pp. 164-171.
6. A. Hastings, Transients: The key to long-term ecological understanding?, Trends Ecol. Evol. 19 (2004), pp. 39-45.
7. J. Ito, A.R. Nikolaev, and C. van Leeuwen, Dynamics of spontaneous transitions between global brain states, Hum. Brain Mapp. 28 (2007), pp. 904-913.
8. L.M. Jones, A. Fontanini, B.F. Sadacca, P. Miller, and D.B. Katz, Natural stimuli evoke dynamic sequences of states in sensory cortical ensembles, Proc. Natl. Acad. Sci. USA 104 (2007), pp. 18772-18777.
9. V.S. Afraimovich, V.P. Zhigulin, and M.I. Rabinovich, On the origin of reproducible sequential activity in neural circuits, Chaos 14 (2004), pp. 1123-1129.
10. M.I. Rabinovich, R. Huerta, and G. Laurent, Transient dynamics for neural processing, Science 321 (2008), pp. 48-50.
11. M.I. Rabinovich, R. Huerta, P. Varona, and V.S. Afraimovich, Transient cognitive dynamics, metastability, and decision making, PLoS Comput. Biol. 4 (2008), p. e1000072.
12. H. Broer, K. Efstathiou, and E. Subramanian, Heteroclinic cycles between unstable attractors, Nonlinearity 21 (2008), pp. 1385-1410.
13. C. Kirst and M. Timme, From networks of unstable attractors to heteroclinic switching, Phys. Rev. E 78 (2008), p. 065201.
14. P. Ashwin and J. Borresen, Discrete computation using a perturbed heteroclinic network, Phys. Lett. A 347 (2005), pp. 208-214.
15. J. Guckenheimer and P. Holmes, Structurally stable heteroclinic cycles, Math. Proc. Cambridge 103 (1988), pp. 189-192.
16. J. Hofbauer, Heteroclinic cycles in ecological differential equations, Tatra Mt. Math. Publ. 4 (1994), pp. 105-116.
17. M. Krupa, Robust heteroclinic cycles, J. Nonlinear Sci. 7 (1997), pp. 129-176.
18. E. Stone and D. Armbruster, Noise and O(1) amplitude effects on heteroclinic cycles, Chaos 9 (1999), pp. 499-506.
19. L.P. Shilnikov, A.L. Shilnikov, D.V. Turaev, and L.O. Chua, World Scientific Series on Nonlinear Science, Series A: Monographs and Treatises, Vol.4, World Scientific Publishing Co. Inc., River Edge, NJ, 1998, pp. xxiv+392.
20. V.S. Afraimovich, M.I. Rabinovich, and P. Varona, Heteroclinic contours in neural ensembles and the winnerless competition principle, Int. J. Bifur. Chaos 14 (2004), pp. 1195-1208.