Analysis of bifurcation phenomena in a 3-cells hysteresis neural network

This paper considers bifurcation phenomena in a simplified hysteresis neural network. The network consists of three cells and has three control parameters. We have discovered that the simple system exhibits various attractors: stable equilibria, periodic orbits, and chaos. Since the system is piecewise linear, the return map and Lyapunov exponents are calculated by using the piecewise exact solution. Using the mapping procedure, the bifurcation mechanism of stable equilibria and three kinds of bifurcation mechanisms of periodic orbits have been clarified. In addition, chaos has been analyzed by using Lyapunov exponents of the return map.