Abstract
A modification of the well-known FitzHugh–Nagumo model with a fast and a slow variable is proposed. The existence and stability of a nonclassical relaxation cycle in this system are studied. The slow component of the cycle is asymptotically close to a discontinuous function, while the fast component is a -like function. Self exciting oscillations in a chain of diffusively coupled neurons as well as in one-dimensional ring of unidirectionally coupled neurons are studied. The existence of an arbitrarily large number of traveling waves for this chain has been shown. In order to illustrate the increase in the number of stable traveling waves, numerical methods are involved.
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