Minimal attractors in digraph system models of neuronal networks

Physica D: Nonlinear Phenomena

Volumn 237, Issue 24, 2008, Pages 3186-3196

  Just, Winfried ^a   Ahn, Sungwoo ^b   Terman, David ^b  

^a OHIO UNIVERSITY   (United States)

^b OHIO STATE UNIVERSITY   (United States)

Author keywords

Attractors; Discrete dynamics; Neuronal networks; Random directed graphs

Indexed keywords

CELLS; CYTOLOGY; DIRECTED GRAPHS; DYNAMICAL SYSTEMS; DYNAMICS; NEURONS; REFRACTORY MATERIALS;

ATTRACTORS; CONNECTION PROBABILITY; DISCRETE DYNAMICAL SYSTEMS; DISCRETE DYNAMICS; NEURONAL NETWORKS; OSCILLATORY BEHAVIORS; RANDOM DIRECTED GRAPHS; RANDOMLY CONNECTED NETWORKS;

NEURAL NETWORKS;

EID: 55149088834     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2008.08.011     Document Type: Article

References (17)

1. Ashwin P., Orosz G., Wordsworth J., and Townley S. Dynamics on networks of cluster states for globally coupled phase oscillators. SIAM J. Appl. Dyn. Syst. 4 (2007) 728-758
2. Bevan M.D., Magill P.J., Terman D., Bolam J.P., and Wilson C.J. Move to the rhythm: Oscillations in the subthalamic nucleus-external globus pallidus network. Trends Neurosci. 25 (2002) 523-531
3. Bollobás B. The evolution of sparse graphs. In: Bollobás B. (Ed). Graph Theory and Combinatorics: Proc. Cambridge Combinatorial Conf. in Honour of Paul Erdo{double acute}s (1984), Academic Press, NY 35-57
4. Derrida B., and Stauffer D. Phase transitions in two-dimensional Kauffman cellular automata. Europhys. Lett. 2 10 (1986) 739-745
5. Destexhe A., and Sejnowski T. Synchronized oscillations in thalamic networks: Insights from modeling studies. In: Steriade M., Jones E., and McCormick D. (Eds). Thalamus vol. II (1997), Elsevier, Amsterdam 331-372
6. Erdo{double acute}s P., and Rényi A. On the evolution of random graphs. Mat. Kutató Int. Közl. 5 (1960) 17-60
7. Golomb D., Wang X.-J., and Rinzel J. Synchronization properties of spindle oscillations in a thalamic reticular nucleus model. J. Neurophysiol. 72 (1994) 1109-1126
8. Hopfield J.J. Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. USA 79 8 (1982) 2554-2558
9. W. Just et al., When can digraph systems be chaotic? 2007 (in progress)
10. W. Just, S. Ahn, D. Terman, Minimal attractors in digraph system models of neuronal networks, MBI Technical Report No. 68. http://mbi.osu.edu/publications/techreports/pub2007.html, 2007 (preprint)
11. Kauffman S.A. Origins of Order: Self-Organization and Selection in Evolution (1993), Oxford U Press
12. Kauffman S., Peterson C., Samuelsson B., and Troein C. Random Boolean network models and the yeast transcriptional network. Proc. Natl. Acad. Sci. USA 100 25 (2003) 14796-14799
13. Pittel B., Spencer J., and Wormald N. Sudden emergence of a giant k-core in a random graph. J. Combin. Theory Ser. B 67 (1996) 111-151
14. Rabinovich M., Volkovskii A., Lecanda P., Huerta R., Abarbanel H.-D., and Laurent G. Dynamical encoding by network of competiing neuron groups: Winnerless competition. Phys. Rev. Lett. 87 (2001) 068102
15. Terman D., Ahn S., Wang X., and Just W. Reducing neuronal networks to discrete dynamics. Physica D 237 (2008) 324-338
16. D. Terman, A. Borisyuk, A. Ahn, X. Wang, B. Smith, Excitation produces transient temporal dynamics in an olfactory network (submitted for publication)
17. Weisbuch G., and Stauffer D. Phase-transition in cellular random Boolean nets. J. Phys. 48 1 (1987) 11-18