The FitzHugh-Nagumo model and spatiotemporal fractal sets based on time-dependent chaos functions

Abstract

It is presented firstly that a one-dimensional (1-D) time-dependent logistic map for population growth is derived from the chaos solution consisting of a time-dependent chaos function, and the logistic map has the dynamics of coherence and incoherence in time, which are the so-called chimera states discussed in the field of complex systems, by introducing the bifurcation diagram and a time-dependent system parameter for the 1-D map as one of non-equilibrium open systems. Secondly, the 2-D time-dependent solvable chaos map corresponding to the FitzHugh-Nagumo model for neural phenomena is obtained on the basis of time-dependent chaos functions, and the 2-D map is shown to have chimera states in time under the assumption of a time-dependent system parameter, and to find spatiotemporal fractal sets defined by initial values as the dynamic stability region for neural cells.