New Chaos Systems Unleashed: Limit-Cycle, Line-Expanding, and Area-Expanding Chaos Revealed!
Manifold Piecewise Constant Systems (MPC) show different types of chaos: limit-cycle, line-expanding chaos, and area-expanding chaos in 2D, 3D, and 4D systems, respectively. The system dynamics simplify into a piecewise-linear return map due to the piecewise-constant nature of the state equation. An evaluation function for the return map helps understand chaos generation, which is supported by theoretical evidence and demonstrated in the lab.