Discrete-Time Chen System: Dynamics, Bifurcation, and Control

What is it about?

The article discusses the qualitative analysis of a discrete-time Chen system, investigating its fixed points, bifurcations, and stability. The system undergoes Neimark-Sacker (NS) and period-doubling (PD) bifurcations when specific parameters vary. The direction and stability of these bifurcations are determined using center manifold theory. The study also utilizes the 0-1 chaos test and hybrid control strategies to eliminate chaotic trajectories in the system. The research focuses on discrete dynamical systems, which have gained attention due to their rich chaotic dynamics and computational efficiency compared to continuous dynamical systems.

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Why is it important?

Advancing the understanding of dynamical systems: This research contributes to the overall understanding of dynamical systems, specifically discrete-time Chen systems, and their bifurcations, which is important for various scientific and engineering disciplines. Chaos control and hybrid control strategies: The study provides insights into chaos control and hybrid control strategies, which are valuable in applications where precise control of complex dynamics is required, such as in robotics, biological systems, and communication networks. Key Takeaways: 1. The research investigates the topological classification, bifurcations, and chaos control of discrete-time Chen systems. 2. The study finds conditions and directions of Neimark-Sacker (NS) and period-doubling (PD) bifurcations in the system, which affect the system's stability and complexity. 3. The existence and local stability of fixed points are analyzed, and the dynamics of the system are found to switch between stable and unstable states, leading to chaos.