Bifurcation Control Based on Van der pol System with Delay

来源 :The Third International Conference on Dynamics,Vibration and | 被引量 : 0次 | 上传用户:liuqin1225
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  The dynamic characteristics of the Van der pol system with delayed are investigated.That is (x)-α(x)(t-τ)(1-βx2) + γx =0 By variable substitution the characteristic equation is obtained.The characteristic equation is λ2-ατλe-λ + γτ 2 =0.The stability of trivial equilibrium is discussed by analyzing distribution of the roots of the associated characteristic equation.lf the system is instability on the equilibrium point.the roots of the characteristic equation should meet Re(λ) =0.From the Re(λ) =0 the result of ω is gotten and the critical values of delay is found.It is found that Hopf bifurcation occurs from trivial equilibrum when the delay passes through critical values.then the critical values and their relations with system parameters are obtained.The effect of time delay on the system is evaluated with numerical method.
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