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Bifurcations of spatiotemporal structures in a medium of FitzHugh-Nagumo neurons with diffusive coupling. (English) Zbl 1380.92012

Summary: We study the boundaries of existence of traveling waves and stationary spatial structures in an active medium model by varying the control parameters. The medium is represented by a ring of diffusively coupled FitzHugh-Nagumo neurons, which, when uncoupled, can demonstrate excitable, self-sustained oscillatory or bistable dynamics depending on control parameter values. The dynamical regimes realized in the medium are compared with those ones observed in an individual FitzHugh-Nagumo neuron. Possible bifurcations of traveling waves are analyzed when the dynamics of the medium elements changes. We also explore the influence of the relaxation level of FitzHugh-Nagumo neurons on the medium dynamics.

MSC:

92C20 Neural biology
34C23 Bifurcation theory for ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models

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