Monotonic width-adjustable pulse control strategy of memristor-based hyper-chaotic Bao system

This paper presents an extension of the three-dimensional Bao system by incorporating a memristor as a feedback element, thereby constructing a four-dimensional hyper-chaotic system. By analyzing the dynamic properties of the system, the study confirms the system’s complex and rich hyper-chaotic behavior. An analog circuit is designed using basic electronic components, validating the consistency between the circuit’s simulated and numerical results. Based on these findings, a novel control strategy is proposed: the monotonic width-adjustable pulse control strategy. The key innovation of this strategy lies in its ability to dynamically adjust the control width sequence in a monotonically varying manner, enhancing both the adaptability and effectiveness of the control process. The exponential stability of the strategy was rigorously verified through mathematical analysis. The effectiveness and practical applicability of the proposed control method are demonstrated by its successful stabilization of the newly developed hyper-chaotic system and its effective regulation of the respiratory disease model.