一个新的混沌系统及其电路仿真

A New Chaotic System and Its Circuit Emulation

构造了一个新的三维自治混沌系统,该系统含有两个参数、两个非线性项.通过理论分析、数值仿真、Lyapunov指数谱和分岔图等非线性动力学分析方法分析了系统的丰富的动力学行为.结果表明系统是耗散的,系统存在两个不稳定平衡点,系统的轨线是有界的,当参数满足一定条件时,系统是混沌的.最后根据新混沌系统的数学模型设计具体的实际电子电路,给出系统处于混沌状态时的电路实验相图,与数值仿真结果是一致的.

A new three-dimensional autonomous chaotic system is constructed in this paper.The new system contains two parameters and two quadratic cross-product terms.The rich dynamics characteristics of the new system are analyzed by means of theoretical analysis and nonlinear techniques,such as numerical simulations,bifurcation diagram and Lyapunov exponent spectrum.Results show this system is dissipative and it has two unstable equilibrium points.The trajectory is bounded and the new system is chaotic when its parameters satisfy certain conditions.Finally,specific practical electronic circuit is designed according to mathematical model of the new chaotic system and the phase diagrams of the circuit under the chaotic state are given,which agree with the simulation results.