Analysis of the limiting behavior of a biological neurons system with delay

Abstract

In this work an analytical and numerical analysis of the limiting behaviors of a system consisting of a pair of biological neurons was carried out. In this case connection between neurons will occur with a delay. As a neuron model, the FitzHugh-Nagumo model was chosen as a model that can reproduce many dynamic behaviors of a real neuron and, at the same time, is not very complex computationally.

Mixed problem for a linear differential equation of parabolic type with nonlinear impulsive conditions

“…Differential equations of mathematical physics have direct applications in the theory of nanosystems (see, for example, [1][2][3][4][5][6][7][8][9][10][11][12][13], and [14]). Partial differential and integro-differential equations of parabolic type with initial and boundary conditions are investigated widely by large number of scientists and have different applications in sciences and technology (see, for example, [15][16][17][18][19][20][21][22][23][24][25][26][27][28]).…”

Inverse problem for a second order impulsive system of integro-differential equations with two redefinition vectors and mixed maxima

“…Subordinate the function x (t) ∈ P C ([0, T ], R n ) in presentation (8) to satisfy the nonlinear two-point boundary condition (3):…”

“…[1][2][3][4][5]. In particular, such kind of problems appear in biophysics at micro-and nano-scales [6][7][8][9][10]. Such differential equations with "discontinuities" at fixed or non-fixed time moments are called differential equations with impulsive effects.…”

Determination of the coefficient function in a Whitham type nonlinear differential equation with impulse effects

“…[1][2][3][4][5]. In particular, such kind of problems appears in biophysics at micro-and nanoscales [6][7][8][9][10]. A lot of publications of studying the differential equations with impulse effects related to various natural and technical processes are appearing [11][12][13][14][15][16][17][18][19][20].…”