Manifold piecewise constant systems and chaos

We propose manifold piecewise constant systems (ab. MPC) and consider basic phenomena: the 2-D, 3-D and 4-D MPCs exhibit limit-cycle, line-expanding c haos and area-expanding chaos, respectively. The right hand side of the sta te equation is piecewise-constant, hence the system dynamics can be simplif ied into a piecewise-linear return map which carl be expressed explicitly I n order to analyze the piecewise-linear return map. we introduce an evaluat ion function for the piecewise-linear return map and give theoretical evide nce for chaos generation. Also the chaotic behaviors are demonstrated in th e laboratory.