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提出一种仅含单个非线性项的四维忆阻混沌系统模型，旨在揭示系统在参数与初始条件变化下的多样动力学行为并实现高效预定义时间同步控制。基于耗散性分析和Lyapunov指数量化，结合参数分岔与多稳态研究，揭示了该系统具有无穷多不稳定平衡点、同构与异构多稳态(点吸引子、周期吸引子与混沌吸引子)分布特征，并发现通过调节忆阻器内部参数可精准实现信号的幅度控制。针对该动力学特性，构建了包含线性与双向幂次非线性衰减项的预定义时间滑模面，利用Lyapunov稳定性理论推导出误差系统在预设时间内收敛的一种新型的充分条件，并设计了可调同步时间上界的双阶段滑模控制律。数值仿真验证表明该系统能够在预定义时间内完成误差收敛，且过程无超调或抖振，具备高精度和强鲁棒性。A four-dimensional memristive chaotic system with only a single nonlinear term is proposed to reveal diverse dynamical behaviors under variations of parameters and initial conditions and to realize efficient synchronization control. Based on dissipativity analysis and Lyapunov exponent computation, combined with bifurcation analysis and multistability exploration, it is shown that the system possesses infinitely many unstable equilibrium points and exhibits both homogeneous and heterogeneous multistability, including point, periodic, and chaotic attractors. Moreover, it is found that amplitude modulation of the system's output signals can be precisely achieved by adjusting internal parameters of the memristor. A predefined-time sliding mode surface with linear and bidirectional power-law nonlinear decay terms is constructed to address synchronization. Sufficient conditions for predefined-time convergence of synchronization errors are derived using Lyapunov stability theory, and a double-stage sliding mode controller with an adjustable upper bound on synchronization time is designed. The resulting control law features an adjustable upper bound for the synchronization time and enables rapid error suppression under arbitrary initial disturbances. Numerical simulations confirm that the synchronization errors converge within the predefined time without overshoot or chattering, demonstrating high precision and strong robustness.
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Keywords:
- Memristive chaotic system /
- multistability /
- amplitude modulation /
- sliding mode control /
- predefined-time synchronization
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