This paper proposes a tool to analyze complicated phenomena from a simple hysteresis network. The simple hysteresis network is described by a piecewise liner ordinal differential equation and has only two parameters: self feedback and DC team. Then this simple system exhibits various kinds of attractors: stable equilibria, periodic orbits, tori and chaos. In order to perform the numerical analysis, we derive return map and propose a fast calculation algorithm for the return map and its Lyapunov exponents based on the exact solutions. Using this algorithm, we have clarified chaos generation and related bifurcation phenomena. Also, we give theoretical formula that give fundamental bifurcation set.