Abstract
In this paper, based on the earlier research, a new fractional-order chaotic Genesio-Tesi model is established. The chaotic phenomenon of the fractional-order chaotic Genesio-Tesi model is controlled by designing two suitable time-delayed feedback controllers. With the aid of Laplace transform, we obtain the characteristic equation of the controlled chaotic Genesio-Tesi model. Then by regarding the time delay as the bifurcation parameter and analyzing the characteristic equation, some new sufficient criteria to guarantee the stability and the existence of Hopf bifurcation for the controlled fractional-order chaotic Genesio-Tesi model are derived. The research shows that when time delay remains in some interval, the equilibrium point of the controlled chaotic Genesio-Tesi model is stable and a Hopf bifurcation will happen when the time delay crosses a critical value. The effect of the time delay on the stability and the existence of Hopf bifurcation for the controlled fractional-order chaotic Genesio-Tesi model is shown. At last, computer simulations check the rationalization of the obtained theoretical prediction. The derived key results in this paper play an important role in controlling the chaotic behavior of many other differential chaotic systems.
Highlights
As is known to us, chaos control issue has been widely studied in the last decades because of its potential practical value in various areas
Is paper mainly focuses on two aspects: (a) designing two appropriate controllers to control the chaotic phenomenon of model (2) and (b) revealing the impact of time delay on the stability and bifurcation behavior of the controlled fractional-order Genesio-Tesi chaotic model. e superiority of this paper can be summarized as follows: (a) A new fractional-order Genesio-Tesi chaotic model is proposed (b) Two controllers are designed to control the chaotic phenomenon of the fractional-order Genesio-Tesi chaotic model (c) e advantages and disadvantages of two controllers are compared e outline of this paper is organized as follows: In Section 2, some elementary knowledge on fractional-order differential is prepared
According to the computer simulation results of model (69) and model (70), we can see that when the time delay remains in a suitable range, the controller chaotic model is locally asymptotically stable, and when the time delay crosses a certain critical value, a Hopf bifurcation appears near the equilibrium point of the controlled model
Summary
As is known to us, chaos control issue has been widely studied in the last decades because of its potential practical value in various areas. In 2009, Sun [22] proposed a tracking control to realize chaos synchronization for the Genesio-Tesi chaotic system (1) based on the time-domain approach. Is paper mainly focuses on two aspects: (a) designing two appropriate controllers to control the chaotic phenomenon of model (2) and (b) revealing the impact of time delay on the stability and bifurcation behavior of the controlled fractional-order Genesio-Tesi chaotic model. (a) A new fractional-order Genesio-Tesi chaotic model is proposed (b) Two controllers are designed to control the chaotic phenomenon of the fractional-order Genesio-Tesi chaotic model (c) e advantages and disadvantages of two controllers are compared e outline of this paper is organized as follows: In Section 2, some elementary knowledge on fractional-order differential is prepared.
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