Dynamical Properties and Synchronizations of a NewChaotic and Hyperchaotic Nonlinear Systems

Abstract

In this thesis, the analysis of hyper-chaos and the optimal control and synchronization of the non-autonomous cardiac conduction system are studied. We mainly analyze, control and synchronize the associated hyper-chaotic behaviors using several methods. More specifically, the relevant nonlinear mathematical model is first presented in the forms of integer and fractional order differential equations. The hyper-chaotic attractions and phase images are then analyzed. Next, efficient optimal control methods are applied to integer and fractional order cases in order to overcome the obnoxious chaotic over-performance. In addition, two identical hyper-chaotic oscillators are synchronized via an adaptive control system and an active controller for integer and fractional mathematical models, respectively. Simulation results confirm that the new nonlinear fractional model shows more flexible behavior than its classical counterpart due to its memory effects. The numerical results are also justified theoretically, and computational experiments demonstrate the effectiveness of the proposed control and synchronization strategies.

In this thesis, the analysis of hyper-chaos and the optimal control and synchronization of the non-autonomous cardiac conduction system are studied. We mainly analyze, control and synchronize the associated hyper-chaotic behaviors using several methods. More specifically, the relevant nonlinear mathematical model is first presented in the forms of integer and fractional order differential equations. The hyper-chaotic attractions and phase images are then analyzed. Next, efficient optimal control methods are applied to integer and fractional order cases in order to overcome the obnoxious chaotic over-performance. In addition, two identical hyper-chaotic oscillators are synchronized via an adaptive control system and an active controller for integer and fractional mathematical models, respectively. Simulation results confirm that the new nonlinear fractional model shows more flexible behavior than its classical counterpart due to its memory effects. The numerical results are also justified theoretically, and computational experiments demonstrate the effectiveness of the proposed control and synchronization strategies.