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Stability of equilibria in an infinite dimensional network of theta neurons

Last modified: 2023-05-15

#### Abstract

We consider an infinite network of identical theta neurons, all-to-all coupled by instantaneous synapses, modelled by a system of delay differential equations. Using the Watanabe-Strogatz ansatz transformation, which reduce the dimension of the infinite network, leading to a three-dimensional system of differential equations, we determine the number of equilibria with respect to some characteristic parameters of the system. Furthermore, we discuss the stability properties of each equilibrium and the possible bifurcations that may take place in the system. Numerical results are also presented to illustrate complex dynamic behavior in this neural system.