Traveling wave solutions of nonlinear scalar integral differential equations arising from synaptically coupled neuronal networks

Linghai Zhang (1) , Axel Hutt (2)

1 Lehigh University
2 NEUROSYS - Analysis and modeling of neural systems by a system neuroscience approach

We consider nonlinear scalar integral differential equations which generalize many important nonlinear scalar integral differential equations arising from synaptically coupled neuronal networks. The synaptic couplings can be very general, including not only pure excitations (modeled with nonnegative kernel functions), lateral inhibitions (modeled with Mexican hat kernel functions), lateral excitations (modeled with upside down Mexican hat kernel functions), but also synaptic couplings which may change sign for finitely many times or even infinitely many times.Moreover, we consider a Heaviside transfer function and distributed transmission and feedback delays. The work studies the existence and stability of traveling front solutions of such equations.

Domaines: Modélisation et simulation

Linghai Zhang, Axel Hutt. Traveling wave solutions of nonlinear scalar integral differential equations arising from synaptically coupled neuronal networks. Journal of Applied Analysis and Computation, 2014, 4 (1), pp.1-68. ⟨hal-00933715⟩