在研究欠阻尼周期势系统时,同时引入乘性高斯白噪声和加性Lévy噪声,首先将二阶欠阻尼周期势系统等价改写为两个一阶随机微分方程,然后借助Janicki-Weron算法产生Lévy噪声序列,并通过数值算法进一步模拟出该系统的稳态概率密...在研究欠阻尼周期势系统时,同时引入乘性高斯白噪声和加性Lévy噪声,首先将二阶欠阻尼周期势系统等价改写为两个一阶随机微分方程,然后借助Janicki-Weron算法产生Lévy噪声序列,并通过数值算法进一步模拟出该系统的稳态概率密度函数(steady-state probability density function,SPD),最后对欠阻尼周期势系统的相变行为进行分析。研究发现系统参数、摩擦系数、稳定性指标、偏斜参数、乘性高斯白噪声强度和加性Lévy噪声强度均可以诱导系统产生相变现象。此外,系统参数和摩擦系数的增大有利于粒子处于稳定状态。展开更多
研究关联噪声与周期信号共同激励下周期势系统的动力学特性.首先利用统一色噪声近似的方法,将二维马尔可夫过程简化为一维非马尔可夫过程,得到了周期势系统的Fokker-Planck(FPK)方程;然后在理论上推导出系统的准稳态概率密度函数(quasi-...研究关联噪声与周期信号共同激励下周期势系统的动力学特性.首先利用统一色噪声近似的方法,将二维马尔可夫过程简化为一维非马尔可夫过程,得到了周期势系统的Fokker-Planck(FPK)方程;然后在理论上推导出系统的准稳态概率密度函数(quasi-steady-state probability density,简称QSPD)的表达式;最后进一步运用4阶龙格库塔算法对QSPD进行数值模拟,分析了噪声及系统各参数对该周期势系统QSPD的影响.展开更多
The principal resonance of Van der Pol-Duffing oscillator to combined deterministic and random parametric excitations is investigated. The method of multiple scales was used to determine the equations of modulation of...The principal resonance of Van der Pol-Duffing oscillator to combined deterministic and random parametric excitations is investigated. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response were studied. Jumps were shown to occur under some conditions. The effects of damping, detuning, bandwidth, and magnitudes of deterministic and random excitations are analyzed. The theoretical analysis were verified by numerical results.展开更多
文摘在研究欠阻尼周期势系统时,同时引入乘性高斯白噪声和加性Lévy噪声,首先将二阶欠阻尼周期势系统等价改写为两个一阶随机微分方程,然后借助Janicki-Weron算法产生Lévy噪声序列,并通过数值算法进一步模拟出该系统的稳态概率密度函数(steady-state probability density function,SPD),最后对欠阻尼周期势系统的相变行为进行分析。研究发现系统参数、摩擦系数、稳定性指标、偏斜参数、乘性高斯白噪声强度和加性Lévy噪声强度均可以诱导系统产生相变现象。此外,系统参数和摩擦系数的增大有利于粒子处于稳定状态。
文摘研究关联噪声与周期信号共同激励下周期势系统的动力学特性.首先利用统一色噪声近似的方法,将二维马尔可夫过程简化为一维非马尔可夫过程,得到了周期势系统的Fokker-Planck(FPK)方程;然后在理论上推导出系统的准稳态概率密度函数(quasi-steady-state probability density,简称QSPD)的表达式;最后进一步运用4阶龙格库塔算法对QSPD进行数值模拟,分析了噪声及系统各参数对该周期势系统QSPD的影响.
文摘The principal resonance of Van der Pol-Duffing oscillator to combined deterministic and random parametric excitations is investigated. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response were studied. Jumps were shown to occur under some conditions. The effects of damping, detuning, bandwidth, and magnitudes of deterministic and random excitations are analyzed. The theoretical analysis were verified by numerical results.
