杜芬振子的仿真分析

Simulation and Analysis of Duffing-equation

混沌系统对微弱信号具有极强的敏感性,同时对噪声具有极大的抑制能力,它的这种性质使得混沌系统具有可应用于小信号检测中的潜力。一个动态非线性系统有四种状态即定态、动态、周期振荡和混沌运动状态,当系统处在一个临界状态,系统参数的一个微小变化也可能引起系统状态的性质变化,即方程的解在相空间的轨迹将发生变化。以杜芬方程作为研究系统,利用MATLAB软件对方程分析、模拟。在临界状态下,系统加入与外力频率相近的单频被测信号,其根轨迹及相平面将发生变化,从而检测出小信号的存在。

Chaotic systems are sensitive to certain signals and immune to noise, at the same time, the properties of which demonstrate their potential application in weak signal detection. There are fore states in a nonlinear system, which is called stationary state, dynamic state, periodic state and chaos. When the system is in the critical state a small perturbation of the system parameters may lead to the qualitative change of the system state. Duffing-equation is chosen as the system to study. MATLAB is used to solve the equation here. When the sine wave signal, which has the similar frequency as the outside force, is added to the system in the critical state, the phase plane diagram and the locus will change. So the weak signal is detected.