分析了乘性和加性噪声作用下三稳态Van der Pol--Duffng振子的随机P分岔.首先用随机平均法得到系统的随机微分方程,求得系统响应幅值的稳态概率密度函数.然后应用分岔分析的奇异性理论,求得随机P分岔发生的临界参数条件,得到多种定性不...分析了乘性和加性噪声作用下三稳态Van der Pol--Duffng振子的随机P分岔.首先用随机平均法得到系统的随机微分方程,求得系统响应幅值的稳态概率密度函数.然后应用分岔分析的奇异性理论,求得随机P分岔发生的临界参数条件,得到多种定性不同的稳态概率密度曲线.讨论了2种激励噪声强度和系统阻尼对响应稳态概率密度曲线峰的个数、各峰值相对大小的影响.通过Monte--Carlo数值模拟对理论计算结果进行了验证.该方法可用于其他系统的随机P分岔分析.展开更多
首先利用多尺度法分析了Duffing-van der Pol系统在多频激励下的主共振响应,得到了该系统的一次近似解。然后利用数值方法研究了系统参数对近似解幅频曲线的影响。最后,运用奇异性理论得到了系统的全部分岔响应曲线,为这一类系统的动态...首先利用多尺度法分析了Duffing-van der Pol系统在多频激励下的主共振响应,得到了该系统的一次近似解。然后利用数值方法研究了系统参数对近似解幅频曲线的影响。最后,运用奇异性理论得到了系统的全部分岔响应曲线,为这一类系统的动态分析与设计提供了理论依据。展开更多
Bifurcations with constraints are open problems appeared in research on periodic bifurcations of nonlinear dynamical systems, but the present singularity theory doesn't contain any analytical methods and results a...Bifurcations with constraints are open problems appeared in research on periodic bifurcations of nonlinear dynamical systems, but the present singularity theory doesn't contain any analytical methods and results about it. As the complement to singularity theory and the first step to study on constrained bifurcations, here are given tire transition sets and persistent perturbed bifurcation diagrams of 10 elementary bifurcation of codimension no more than three.展开更多
The normal forms of coupling functions governing local and global bifurcations are studied for a generic (d+1) -parameter family of three-dimensional systems with a heteroclinic orbit connecting a hyperbolic saddle an...The normal forms of coupling functions governing local and global bifurcations are studied for a generic (d+1) -parameter family of three-dimensional systems with a heteroclinic orbit connecting a hyperbolic saddle and a nonhyperbolic equilibrium occurring in the saddle-node,transcritical and pitchfork bifurcations,respectively.Singularity theory and a version of Melnikov function are used in this paper.展开更多
文摘分析了乘性和加性噪声作用下三稳态Van der Pol--Duffng振子的随机P分岔.首先用随机平均法得到系统的随机微分方程,求得系统响应幅值的稳态概率密度函数.然后应用分岔分析的奇异性理论,求得随机P分岔发生的临界参数条件,得到多种定性不同的稳态概率密度曲线.讨论了2种激励噪声强度和系统阻尼对响应稳态概率密度曲线峰的个数、各峰值相对大小的影响.通过Monte--Carlo数值模拟对理论计算结果进行了验证.该方法可用于其他系统的随机P分岔分析.
文摘Bifurcations with constraints are open problems appeared in research on periodic bifurcations of nonlinear dynamical systems, but the present singularity theory doesn't contain any analytical methods and results about it. As the complement to singularity theory and the first step to study on constrained bifurcations, here are given tire transition sets and persistent perturbed bifurcation diagrams of 10 elementary bifurcation of codimension no more than three.
基金Project supported by the National Natural Science Foundation of ChinaState Education Commission Foundation
文摘The normal forms of coupling functions governing local and global bifurcations are studied for a generic (d+1) -parameter family of three-dimensional systems with a heteroclinic orbit connecting a hyperbolic saddle and a nonhyperbolic equilibrium occurring in the saddle-node,transcritical and pitchfork bifurcations,respectively.Singularity theory and a version of Melnikov function are used in this paper.
