推广恒Lyapunov指数谱混沌系统及其演变研究

基于恒Lyapunov指数谱改进系统，通过在系统方程中添加线性项与常数项，实现了恒Lyapunov指数谱混沌系统的推广.首先结合Lyapunov指数谱、分岔图和状态变量幅值演变的数值仿真，揭示了该系统的动力学行为；接着通过组合不同的线性项，从推广系统演变得到一族性质类似而又相轨不同的子系统，并分析了各个子系统的平衡点、特征值与Lyapunov指数等动力学特征；最后，指出该系统在混沌雷达、保密通信和其他信息处理系统中具有广阔的应用前景. 关键词： 推广混沌系统 Lyapunov指数谱 演变 子系统

An extension system with constant Lyapunov exponent spectrum and its evolvement

By introducing linear terms and constant terms in dynamic equations, the extension system with constant Lyapunov exponent spectrum is proposed based on the improved constant-Lyapunov-exponent-spectrum system. Firstly, the dynamical behaviour of the extension system is investigated and expounded by simulation of Lyapunov exponent spectrum, bifurcation diagram and numerical analysis on amplitude evolvement of state variables. Secondly, a class of subsystems with the same properties but different phase trajectories is obtained through different combinations of linear terms from the extension system. The dynamical characteristics including equilibrium, eigenvalue and Lyapunov exponents are analyzed in detail simultaneously. Finally, it is pointed out that the chaotic system will have a tremendous application prospect in chaotic radar, secure communications and other information processing systems.