Dynamics of a simple hysteresis network

In order to approach the explication of rich dynamics from a large scale nonlinear network, this paper analyses a continuous time hysteresis network whose cross connection is uniform. This system has only two parameters. Applying an efficient piecewise linear technique for a binary hysteresis element, we can clarify the existence condition of periodic orbits and the number of them. Also we can prove a sufficient condition for local convergence. In addition, the global convergence is verified by both numerical and laboratory experiments