Input-Output Mechanism of the Discrete Chaos Extension

In this chapter the extension of chaos in difference equations is discussed. The theoretical results are based on chaos in the sense of Devaney and period-doubling cascades. The existence of homoclinic and heteroclinic orbits is rigorously proved, and a theoretical control technique for the extended chaos is proposed. The results are supported with the aid of simulations. Arbitrarily high-dimensional chaotic discrete-time dynamical systems can be designed by means of the presented technique. A discrete gonorrhea model is utilized to generate chaotic behavior in population dynamics.