In this paper, we make some analysis on the FitzHugh-Nagumo model and improve it to build a neural network, and the network is used to implement visual selection and attention shifting. Each group of neurons representing one object of a visual input is synchronized; different groups of neurons representing different objects of a visual input are desynchronized. Cooperation and competition mecha...

Chaos is an important applied area in nonlinear dynamical systems and it is applicable to many real-world systems including the biological systems. Nerve membranes are known to exhibit their own nonlinear dynamics which generate and propagate action potentials. Such nonlinear dynamics in nerve membranes can produce chaos in neurons and related bifurcations. In 1952, A.L. Hodgkin and A.F. Huxley...

We provide an asymptotically justified derivation of activity measure evolution equations (AMEE) for a finite size neural network. The approach takes into account the dynamics for each isolated neuron in the network being modeled by a biophysical model, i.e. Hodgkin-Huxley equations or their reductions. By representing the interacting network as self and pairwise interactions, we propose a gene...

The work concerns the multiscale modeling of a nerve fascicle myelinated axons. We present rigorous derivation macroscopic bidomain model describing behavior electric potential in based on FitzHugh–Nagumo membrane dynamics. approach is two-scale convergence machinery combined with method monotone operators.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Chapter 1 Preliminary concepts and literature review . . . . . . . . . . . . . . . 11 1.1 Cellular excitability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.1.1 Membranes, ionic gradients, and transport . . . . . . . . . . . . . 12 1.1.2 Electrical signaling and action potentials . . . . . . . . . . ...

In this paper we study a system of nonlinear diffusion equations on a finite network in the presence of an impulsive noise acting on the nodes of the system. We allow a rather general nonlinear drift term, including dissipative functions of FitzHugh-Nagumo type (i.e. f(u) = −u(u− 1)(u− a)) arising in various models of neurophysiology (see e.g. the monograph [19] for more details). Electric sign...

This paper describes the identification of a temperature dependent FitzHugh–Nagumo model directly from experimental observations with controlled inputs. By studying the steady states and the trajectory of the phase of the variables, the stability of the model is analyzed and a rule to generate oscillation waves is proposed. The dependence of the oscillation frequency and propagation speed on th...