具有多种平衡点类型的新型三维混沌系统

New three-dimensional chaotic system with multiple types of equilibrium points

基于Lü系统设计了一个新型三维连续混沌系统,详细分析了此系统的动力学特性。系统的重要特性是在给定系统参数值,且不改变系统状态方程中的任何非线性项或线性项的情形下,系统具有一个稳定平衡点、一个不稳定平衡点和线平衡点;同时存在混沌吸引子、周期吸引子和稳定点吸引子共存,拟周期吸引子与周期吸引子共存,周期吸引子与周期吸引子共存等多稳定性现象。设计并仿真了此系统基于Multisim的模拟电路和基于FPGA的数字电路,表明了系统的可实现性。此外,用系统产生伪随机序列,并通过了实验验证。

Based on the Lüsystem,a new three-dimensional continuous chaotic system with multiple types of equilibrium points is proposed and analyzed in detail in this paper.The system’s important property is that there are a stable equilibrium point,an unstable equilibrium point and a line equilibrium with a given value of system parameter and without changing any nonlinear items or linear items in the system’s state equation.Meanwhile,there are the coexistence of chaotic attractor,periodic attractor and stable point,the coexistence of quasi-periodic and periodic attractor,and the coexistence of two different periodic attractors.The analog circuit based on Multisim and the digital circuit based on FPGA are designed and simulated,and the practicability of the system is proved.In addition,a pseudorandom sequence based on the system is also produced and verified.