Anticontrol of chaos via feedback

In this paper, a simple control method that combines a linear state-feedback with a nonlinear mod-operation is proposed for making an arbitrarily given, deterministic, discrete-time dynamical systems chaotic. The given system can be arbitrary in the sense that it can be either linear or nonlinear, lower or higher-dimensional, asymptotically stable, unstable, or chaotic. The resulting controlled system is chaotic in the sense that the controlled map (1) has sensitive dependence on initial conditions, (2) is topologically transitive, and (3) has a dense set of periodic points.