含间隙多约束碰撞振动系统稳定性分析

针对一类单自由度含间隙多约束碰撞振动系统，通过在碰撞面处建立系统的Poincaré 映射，推导系统的Jacobi 矩阵，将连续动力系统转换为离散动力系统，并利用Gram-Schmidt 正交化和范式归一化计算得到系统的Lyapunov 指数谱。通过数值模拟，计算系统混沌吸引子与周期吸引子的收敛序列，结合系统相图、单参分岔图及Lyapunov 指数 谱，分析系统周期运动稳定性及各类分岔现象，通过控制系统参数双向变化发现相邻周期运动间存在的周期共存现 象，验证该计算方法的有效性和正确性，研究成果可为后续针对该系统的混沌判断及混沌控制提供理论依据。

Adaptive Anti-Synchronization of New Hyperchaotic System

This paper constructs a new four-dimensional continuous autonomous hyperchaotic system. The basic dynamical behaviors of this hyperchaotic system are investigated, a circuit diagram is designed for verifying the hyperchaotic behaviors, and some simulation observations are given. Moreover, an adaptive control method and a parameter update rule for unknown parameters based on Lyapunov stability theory are introduced to achieve anti-synchronization of two systems. Finally, the numerical simulations are shown to verify the results.