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| Dynamical Analysis of a New Chaotic System and Its Sliding Mode Control |
| ZHANG Hong, ZHANG Fuchen
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| Chongqing Key Laboratory of Statistical Intelligent Computing and Monitoring, School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China |
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Abstract This paper proposes a novel three-dimensional autonomous chaotic system in order to discover more chaotic behaviors in electrons and circuits, which includes four parameters and three nonlinear coupling terms. Based on the Lagrangian stability theory, the quantitative estimate expression of the ultimate bound of this system was strictly derived by constructing the generalized Lyapunov function. A new sliding mode control strategy was designed based on the Vaidyanathan theorem, achieving global asymptotic synchronization of the system. The research results show that the system has a global exponential attractive set. Numerical simulation verifies the strong robustness and fast convergence of the sliding mode control, and its performance is superior to the adaptive control. This achievement not only enriches the theory of chaotic systems but also provides an effective control method for engineering applications.
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Received: 23 June 2025
Published: 19 May 2026
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