Analysis reveals adaptive control enhances synchronization of hyperchaotic systems, indicating a novel approach using passivity theory.
A five‐dimensional hyperchaotic system is proposed based on a three‐dimensional autonomous chaotic system by introducing two new variables. Based on Lyapunov stability theory and passivity theory, the investigation looks into passivity‐based adaptive chaotic synchronization. Through theoretical analysis and numerical simulation, the dissipation, phase diagrams, Lyapunov exponents, and bifurcation diagrams of the system were studied in detail to analyze its dynamic characteristics. The analog circuit simulation of the new five‐dimensional system is carried out by Multisim. The simulation results are verified by comparing them with the numerical simulation results in MATLAB. The adaptive control method combines passive and adaptive control theories to provide a new perspective and solution for the synchronization control of chaotic systems. The parameter estimation and updating laws not only improve the flexibility of synchronization control but also provide strong support for subsequent experimental studies and practical applications. The effectiveness of the proposed method is verified by numerical simulation, which proves that the method performs well in coping with the synchronization problem of complex hyperchaotic systems with uncertain parameters.
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Zhou et al. (2025) studied this question.
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