本文研究含参数激励耦合van der Pol系统的同伦分析方法和多尺度方法及其在共振问题上的应用。首先,利用多尺度方法讨论系统发生1∶1主共振,1∶2超谐波共振,得到它们的平均方程,发现其存在复杂的周期运动。同时,运用同伦分析方法研究参...
详细信息
本文研究含参数激励耦合van der Pol系统的同伦分析方法和多尺度方法及其在共振问题上的应用。首先,利用多尺度方法讨论系统发生1∶1主共振,1∶2超谐波共振,得到它们的平均方程,发现其存在复杂的周期运动。同时,运用同伦分析方法研究参数激励系统的非线性振动响应,给出了系统周期解的解析逼近。最后,把运用同伦分析方法和多尺度方法得到解析近似解与数值结果进行比较,结果表明同伦分析方法和多尺度方法是求解参数激励非线性共振系统的有效方法。
In 1979,*** has pointed out that the conventional treatment of the simplest self-exciting homopolar disc dynamo has inconsistencies because of the neglect of induced azimuthal eddy currents,which can be resolved by in...
In 1979,*** has pointed out that the conventional treatment of the simplest self-exciting homopolar disc dynamo has inconsistencies because of the neglect of induced azimuthal eddy currents,which can be resolved by introducing a segmented disc *** we return to the simple dynamo system proposed by Moffatt,and demonstrate previously unknown hidden chaotic *** we study multistability and coexistence of three types of attractors in the autonomous dynamo system in three dimensions:equilibrium points,limit cycles and hidden chaotic *** addition,the existence of two homoclinic orbits is proved rigorously by the generalized Melnikov ***,by using Poincare compactification of polynomial vector fields in three dimensions,the dynamics near infinity of singularities is obtained.
暂无评论