Informatica

In this paper, the nonlinear neural network FitzHugh–Nagumo model with an expansion by the excited neuronal kernel function has been investigated. The mean field approximation of neuronal potentials and recovery currents inside neuron ensembles was used. The biologically more realistic nonlinear sodium ionic current–voltage characteristic and kernel functions were applied. A possibility to present the nonlinear integral differential equations with kernel functions under the Fourier transformation by partial differential equations allows us to overcome the analytical and numerical modeling difficulties. An equivalence of two kinds solutions was confirmed basing on the errors analysis. The approach of the equivalent partial differential equations was successfully employed to solve the system with the heterogeneous synaptic functions as well as the FitzHugh–Nagumo nonlinear time-delayed differential equations in the case of the Hopf bifurcation and stability of stationary states. The analytical studies are corroborated by many numerical modeling experiments.