Probabilistic characterization of chaotic behavior in a family of feedback control systems

The authors investigate a family of two-dimensional nonlinear feedback systems which do not satisfy the Lipschitz continuity condition and exhibit chaotic behavior. The geometric Poincare map. is determined analytically and a bifurcation study in terms of two canonical parameters and the associated asymptotic behavior of the systems are presented. Ergodic theory of one-dimensional dynamic systems is used to derive a probabilistic description of the chaotic motions inside the chaotic attractor. It is shown that the chaotic motion is isometric to an experiment of randomly tossing an uneven die