Zhu Yingfang, Hu Yuan, Zhu Erxi
College of Internet of Things Engineering, Jiangsu Vocational College of Information Technology, Wuxi, Jiangsu, China.
John B. and Lillian E. Neff College of Business and Innovation, University of Toledo, Toledo, Ohio, United States of America.
PLoS One. 2025 Jun 3;20(6):e0324331. doi: 10.1371/journal.pone.0324331. eCollection 2025.
Chaos has emerged as a significant area of research, with the control of chaotic systems being central to this field. This study proposes a novel trigonometric feedback control strategy to regulate Hopf bifurcation in a four-dimensional hyperchaotic system featuring coexisting attractors. By introducing a nonlinear controller [Formula: see text], we establish the stability criteria for equilibrium points under the parameter space a>0, b>0, and [Formula: see text]. Theoretical analysis reveals that the system undergoes a supercritical Hopf bifurcation at [Formula: see text], leading to the emergence of stable limit cycles. Numerical simulations validate the control efficacy: periodic oscillations are observed at d = -1, while equilibrium convergence is achieved at d = -3. Phase portrait analysis and Lyapunov exponent spectra confirm the suppression of chaotic dynamics. This work advances the theoretical framework for bifurcation control in high-dimensional chaotic systems and offers practical implications for secure communication applications.
混沌已成为一个重要的研究领域，混沌系统的控制是该领域的核心。本研究提出了一种新颖的三角反馈控制策略，以调节具有共存吸引子的四维超混沌系统中的霍普夫分岔。通过引入非线性控制器[公式：见原文]，我们在参数空间a>0、b>0和[公式：见原文]下建立了平衡点的稳定性判据。理论分析表明，该系统在[公式：见原文]处经历超临界霍普夫分岔，导致稳定极限环的出现。数值模拟验证了控制效果：在d = -1时观察到周期振荡，而在d = -3时实现了平衡点收敛。相图分析和李雅普诺夫指数谱证实了对混沌动力学的抑制。这项工作推进了高维混沌系统中分岔控制的理论框架，并为安全通信应用提供了实际意义。
