Duffing振子和Van der Pol振子耦合的动力学行为分析

Analysis of Dynamical Behavior of a Van Der Pol Oscillator Coupled to a Duffing Oscillator

中文关键词:混沌  耦合振子  微弱信号检测  仿真

英文关键词:chaos  coupling oscillators  weak signal detection  simulation

中文摘要:

      针对耦合非线性混沌振子复杂的动力学行为，本文将Duffing振子和Van der Pol振子进行耦合，建立了Duffing振子和Van der Pol振子的耦合模型。与单个振子相比，耦合Duffing振子和Van der Pol振子表现出了更加丰富的动力学特性，采用Simulink仿真的方法，通过不同策动力幅值、不同耦合系数、不同频率下耦合非线性振子的相图和庞加莱截面图分析了耦合非线性振子的动力学行为，研究了耦合振子对微弱周期信号的敏感性和对噪声的免疫力，并将此模型应用于微弱信号检测的研究中。

英文摘要:

      For complex dynamic behaviors of coupling nonlinear chaotic oscillators, this paper makes a Van der Pol oscillator couple to a duffing oscillator and establishes a duffing oscillator and Van der Pol oscillator coupling model, which, compared with the single oscillator, shows rich dynamics. With Simulink simulation method, by coupling the phase diagrams and Poincaré maps of nonlinear chaotic oscillators under different amplitudes of the driving motivation, different coupling coefficients and different frequencies, this paper analyzes the dynamics of coupling nonlinear oscillators, and studies the coupling oscillator sensitivity to the weak periodic signals and the immunity of noise and has applied this model in weak signal detection.