Abstract
In this paper, the hyperchaos analysis, optimal control, and synchronization of a nonautonomous cardiac conduction system are investigated. We mainly analyze, control, and synchronize the associated hyperchaotic behaviors using several approaches. More specifically, the related nonlinear mathematical model is firstly introduced in the forms of both integer- and fractional-order differential equations. Then the related hyperchaotic attractors and phase portraits are analyzed. Next, effectual optimal control approaches are applied to the integer- and fractional-order cases in order to overcome the obnoxious hyperchaotic performance. In addition, two identical hyperchaotic oscillators are synchronized via an adaptive control scheme and an active controller for the integer- and fractional-order mathematical models, respectively. Simulation results confirm that the new nonlinear fractional model shows a more flexible behavior than its classical counterpart due to its memory effects. Numerical results are also justified theoretically, and computational experiments illustrate the efficacy of the proposed control and synchronization strategies.
Highlights
1 Introduction Chaos is one of the most prominent features of nonlinear dynamical systems whose state variables are highly dependent on its initial conditions. This dependency leads to the divergent behavior of such systems, the fact which reveals the great importance of detailed study regarding chaotic phenomena
3.1.2 Fractional-order case we propose an optimal chaos controller in order to diminish the hyperchaotic behaviors of the nonautonomous cardiac conduction system modeled by the fractional-order dynamical equations (10)
4 Discussions and concluding remarks In this paper, the hyperchaotic behaviors of a nonautonomous cardiac conduction system were investigated in both frames of integer- and fractional-order differential equations
Summary
Chaos is one of the most prominent features of nonlinear dynamical systems whose state variables are highly dependent on its initial conditions. In [31], the authors synchronized the chaotic behavior of fractional-order systems according to the stability conditions and using a feedback control method. We synchronize two identical hyperchaotic oscillators in the frameworks of both classical and fractional equations by applying an adaptive controller and an active compensator, respectively.
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