Manifold Piecewise Constant Systems and Chaos

SUMMARY We propose manifold piecewise constant systems (ab. MPC) and consider basic phenomena: the 2-D, 3-D and 4-DMPCs exhibit limit-cycle, line-expanding chaos and areaexpanding chaos, respectively. The righthand side of the state equation is piecewise-constant, hence the system dynamics can be simplified into a piecewise-linear return map which can be expressed explicitly. In order to analyze the piecewise-linear return map, we introduce an evaluation function for the piecewise-linear return map and give theoretical evidence for chaos generation. Also the chaotic behaviors are demonstrated in the laboratory.