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Complex bifurcation structures in the Hindmarsh-Rose neuron model. (English) Zbl 1185.37189

Summary: The results of a study of the bifurcation diagram of the Hindmarsh-Rose neuron model in a two-dimensional parameter space are reported. This diagram shows the existence and extent of complex bifurcation structures that might be useful to understand the mechanisms used by the neurons to encode information and give rapid responses to stimulus. Moreover, the information contained in this phase diagram provides a background to develop our understanding of the dynamics of interacting neurons.

MSC:

37N25 Dynamical systems in biology
92C20 Neural biology
37G99 Local and nonlocal bifurcation theory for dynamical systems
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[1] DOI: 10.1126/science.1097725
[2] Birkhoff G., A Survey of Modern Algebra (1996)
[3] DOI: 10.1142/S0218127498000681 · Zbl 0932.92008
[4] DOI: 10.1016/0167-2789(85)90060-0 · Zbl 0582.92007
[5] DOI: 10.1103/PhysRevLett.92.074104
[6] DOI: 10.1016/S0006-3495(61)86902-6
[7] Foss J., J. Neurophysiol. 84 pp 975–
[8] DOI: 10.1063/1.1594851 · Zbl 1080.92505
[9] DOI: 10.1142/p352
[10] DOI: 10.1103/PhysRevE.72.051922
[11] Guckenheimer J., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (2002)
[12] DOI: 10.1016/S0167-2789(01)00290-1 · Zbl 1026.92008
[13] DOI: 10.1098/rspb.1984.0024
[14] Hirsch M. W., Differerential Equations, Dynamical Systems, and An Introduction to Chaos (2004)
[15] DOI: 10.1113/jphysiol.1952.sp004764
[16] DOI: 10.1142/S0218127405013678 · Zbl 1092.37500
[17] DOI: 10.1103/PhysRevLett.93.214101
[18] DOI: 10.1017/CBO9780511803260 · Zbl 1006.37001
[19] DOI: 10.1103/PhysRevE.72.031909
[20] DOI: 10.1103/PhysRevLett.92.114102
[21] DOI: 10.1038/376021a0
[22] DOI: 10.1038/35067550
[23] DOI: 10.1016/0167-2789(85)90011-9 · Zbl 0585.58037
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