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Integer and fractional general \(T\)-system and its application to control chaos and synchronization. (English) Zbl 1433.34083

Summary: We propose a three-dimensional autonomous nonlinear system, called the general \(T\) system, which has potential applications in secure communications and the electronic circuit. For the general \(T\) system with delayed feedback, regarding the delay as bifurcation parameter, we investigate the effect of the time delay on its dynamics. We determine conditions for the existence of the Hopf bifurcations and analyze their direction and stability. Also, the fractional order general \(T\)-system is proposed and analyzed. We provide some numerical simulations, where the chaos attractor and the dynamics of the Lyapunov coefficients are taken into consideration. The effectiveness of the chaotic control and synchronization on schemes for the new fractional order chaotic system are verified by numerical simulations.

MSC:

34H10 Chaos control for problems involving ordinary differential equations
34A08 Fractional ordinary differential equations
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