研究了时滞及时滞反馈控制参数对Van der Pol系统极限环幅值的影响.运用自适应的平均场近似方法给出了系统的线性化近似及系统参数Lyapunov稳定性的边界条件,同时给出了Van der Pol系统的关联时间和功率谱密度的数值模拟结果.通过与平均场近似下的解析结果比较后发现,数值模拟结果和理论结果符合.进一步讨论了时滞反馈控制参数、噪声强度以及时滞对关联时间和功率谱密度的影响.
研究了Van der Pol-Duffing单边约束系统在谐和与随机噪声联合激励下的响应问题。用多尺度法分离了系统的快变项,讨论了系统的阻尼项、非线性项和随机项等参数对系统响应的影响。在一定条件下,当约束距离较大时对应于不同的初始条件,系统具有两个非碰撞的稳态响应;而当约束距离不大时,对应于不同的初始条件,系统也可以有两个不同的稳态响应,其中一个是发生碰撞的响应,而另外一个则不发生碰撞。随机扰动可以使得系统的响应从一个极限环变为一扩散的极限环。数值模拟表明本文提出的方法是有效的。
In this paper, a double obstacle problem of variational inequalities is considered and its solutions is obtained. The results of one-sided obstacle problem are not required in the analysis of our main results, which is different from the previous works.
The exponential p-moment stability of stochastic impulsive differential equations is addressed. A new theorem to ensure the p-moment stability is established for the trivial solution of the stochastic impul- sive differential system. As an application of the theorem proposed, the problem of controlling chaos of Lorenz system which is excited by parameter white-noise excitation is considered using impulsive control method. Finally, numerical simulation results are given to verify the feasibility of our approach.
