Stability switches,oscillatory multistability,and spatio-temporal patterns of nonlinear oscillations in recurrently delay coupled neural networks |
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Authors: | Yongli Song Valeri A Makarov Manuel G Velarde |
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Institution: | (1) Instituto Pluridisciplinar, Universidad Complutense, Paseo Juan XXIII, 1, 28040 Madrid, Spain;(2) Department of Mathematics, Tongji University, 200092 Shanghai, China;(3) Depto. de Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense, Avda. Complutense s/n, 28040 Madrid, Spain |
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Abstract: | A model of time-delay recurrently coupled spatially segregated neural assemblies is here proposed. We show that it operates
like some of the hierarchical architectures of the brain. Each assembly is a neural network with no delay in the local couplings
between the units. The delay appears in the long range feedforward and feedback inter-assemblies communications. Bifurcation
analysis of a simple four-units system in the autonomous case shows the richness of the dynamical behaviors in a biophysically
plausible parameter region. We find oscillatory multistability, hysteresis, and stability switches of the rest state provoked
by the time delay. Then we investigate the spatio-temporal patterns of bifurcating periodic solutions by using the symmetric
local Hopf bifurcation theory of delay differential equations and derive the equation describing the flow on the center manifold
that enables us determining the direction of Hopf bifurcations and stability of the bifurcating periodic orbits. We also discuss
computational properties of the system due to the delay when an external drive of the network mimicks external sensory input. |
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Keywords: | Neural network Delay Hopf bifurcation Stability Spatio-temporal pattern |
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