具有隐藏吸引子的混沌系统的统一广义投影同步

Unified Generalized Projection Synchronization of Chaotic Systems with Hidden Attractors

针对一个四维非线性动力系统,通过分析其平衡点发现,该系统存在由无穷平衡点构成的平衡点线,因此其吸引子属于隐藏吸引子范畴.基于Lyapunov稳定性理论,构造不同的同步误差系统,设计合适的控制器,实现不同的同步方式,如完全同步、反同步、错乱广义投影同步以及统一广义投影同步等,并通过MATLAB数值模拟验证其有效性.

By analyzing the equilibrium point of a four-dimensional nonlinear dynamic system,it is found that there is an equilibrium line composed of infinite equilibrium points,so its attractor can be defined as hidden attractor.Based on Lyapunov stability theory,different synchronization error systems are constructed,and appropriate controllers are designed to realize different synchronization modes,such as full synchronization,anti-synchronization,disordered generalized projection synchronization and unified generalized projective synchronization.The effectiveness of these synchronization methods is verified by MATLAB numerical simulation.