Deterministic and random synthesis of discrete chaos

In this paper, two anticontrol algorithms for synthesis of discrete chaos are introduced. In these algorithms, the control parameter of a discrete dynamical system is switched, either randomly or in a deterministic way, between two or more values corresponding to periodic motions, the result being chaotic behavior. These algorithms require no knowledge of specific mathematical properties of the underlying map modeling the system. The existence of chaos is demonstrated using various tools including graphical iteration, histogram, Lyapunov exponent and surrogate tests. In this paper, these very simple and implementable chaotifiers are applied to the logistic map.