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Input-Output Mechanism of the Discrete Chaos Extension

2014-08-09
Akhmet, Marat
Fen, Mehmet Onur
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.