Distribution of controlled Lyapunov exponents: a statistical simulation study

A feedback control design method was proposed in Chen and Lai (1996, Internat. J. Bifur, Chaos 6, 1341–1349) towards anti-control of chaos by means of making an arbitrary discrete-time dynamical system behave chaotically, where the feedback control can force all the Lyapunov exponents of the controlled system become strictly positive. Since a control sequence so designed is not uniquely determined, random mechanism can be used to select a suitable control-gain sequence. The behavior (distribution) of the controlled Lyapunov exponents generated by the proposed method is important and hence calls for further statistical analysis. Using Monte Carlo simulations, we examine the distribution empirically in this paper.