Conclusions


A simple 4-dimensional piecewise-linear system was presented. 

It exhibits chaotic behavior for a wide range of the parameter values, and typical bifurcations are observed. Because the system is piecewise-linear, we can quickly predict the bifurcations of the periodic solution by matrix calculations.

It is one of the practical good ways to quickly predict the bifurcation of the periodic solution if the computation of the exponential of matrices are easily possible.