Complex dynamics in an ideal commutable pendulum

This paper shows complex dynamical behavior in an ideal commutable pendulum. This system is set with two regions of different natural frequencies and complex behavior is present by commuting from one region to the other under certain rules. This commutable commutable pendulum shows a very complex behavior besides the fact that it is based on a simple pendulum model. By varying a single parameter in the model, this commutable pendulum may have simple limit cycle, complex limit cycle and a chaotic behavior. Same complex behavior is extended to mimic other chaotic maps.