Stability, bifurcation, and multistability in a system of two coupled neurons with multiple time delays. (English) Zbl 0992.92013

Summary: A system of delay differential equations representing a model for a pair of neurons with time-delayed connections between the neurons and time delayed feedback from each neuron to itself is studied. Conditions for the linear stability of the trivial solution of this system are represented in a parameter space consisting of the sum of the time delays between the elements and the product of the strengths of the connections between the elements. It is shown that the trivial fixed point may lose stability via a pitchfork bifurcation, a Hopf bifurcation, or one of three types of codimension-two bifurcations. Multistability near these latter bifurcations is predicted using center manifold analysis and confirmed using numerical simulations.


92C20 Neural biology
34K20 Stability theory of functional-differential equations
34K18 Bifurcation theory of functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
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