Dynamical modeling demonstrates global exponential synchronization in a 4D chaotic system, highlighting effective parameter boundaries for robust chaos control.
Bifurcation is one of the pathways through which nonlinear dynamical systems transition into chaotic states. Synchronization control is a method for controlling chaos in nonlinear dynamical systems. The Hopf bifurcation characteristics of a four-dimensional (4D) chaotic system are analyzed. The relationship between the Hopf bifurcation characteristics and the parameters is determined using high-dimensional bifurcation theory, and the stability of the bifurcation periodic solutions of the system is assessed. By analyzing the global exponential attractor, the global boundedness of the system is proved. Based on the global exponential attractor and Dini derivative, a linear controller is set up through system configuration to perform global exponential synchronization control on the drive and response systems of a 4D chaotic system. The range of control parameter values is obtained. By taking values within the range of control parameters, the goal of synchronous control can be achieved. The correctness of the theoretical analysis is verified through numerical simulation analysis.
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