Chaos Control for a Fractional-Order Jerk System via Time Delay Feedback Controller and Mixed Controller
Open Access
- 5 December 2021
- journal article
- research article
- Published by MDPI AG in Fractal and Fractional
- Vol. 5 (4), 257
- https://doi.org/10.3390/fractalfract5040257
Abstract
In this study, we propose a novel fractional-order Jerk system. Experiments show that, under some suitable parameters, the fractional-order Jerk system displays a chaotic phenomenon. In order to suppress the chaotic behavior of the fractional-order Jerk system, we design two control strategies. Firstly, we design an appropriate time delay feedback controller to suppress the chaos of the fractional-order Jerk system. The delay-independent stability and bifurcation conditions are established. Secondly, we design a suitable mixed controller, which includes a time delay feedback controller and a fractional-order PDσ controller, to eliminate the chaos of the fractional-order Jerk system. The sufficient condition ensuring the stability and the creation of Hopf bifurcation for the fractional-order controlled Jerk system is derived. Finally, computer simulations are executed to verify the feasibility of the designed controllers. The derived results of this study are absolutely new and possess potential application value in controlling chaos in physics. Moreover, the research approach also enriches the chaos control theory of fractional-order dynamical system.Keywords
Funding Information
- National Natural Science Foundation of China (61673008, 62062018)
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