两类非光滑系统的极限环研究

发布时间：2018-05-15 22:13

本文选题：钟摆 + 极限环　；参考：《江苏大学》2017年硕士论文

【摘要】：分段光滑系统作为一类典型的非线性系统,其相关的理论在自然科学和社会科学领域都有广泛的应用,许多科学问题都需要用分段光滑动力系统理论来分析研究。本文以带有干摩擦和冲击效应的钟摆为研究背景,探索了一般的钟摆模型的极限环的存在性。首先结合Filippov系统刻画语言,解释了当钟摆进行无外加能量补充的小摆角摆动时,钟摆最终会停止在滑动集上的原因。其次,利用数值模拟的方法,给出钟摆系统在有能量补充时,存在极限环的能量满足条件,并结合环域定理证明了一般的钟摆模型存在唯一稳定的极限环。最后,本文在含参数分段线性系统的极限环存在的基础上,研究了一类含参数分段非线性系统,当参数从大于0变化到小于0过程中,系统的平衡点由结点移动到焦点时,系统极限环存在的条件及证明。
[Abstract]:As a typical nonlinear system, piecewise smooth systems are widely used in both natural and social sciences. Many scientific problems need to be analyzed and studied by piecewise smooth dynamical system theory. Based on the pendulum with dry friction and impact effects, the existence of limit cycles of general pendulum models is explored in this paper. Firstly, with the Filippov system description language, it is explained why the pendulum will eventually stop on the sliding set when the pendulum oscillates at a small angle without additional energy. Secondly, by using the numerical simulation method, we give the condition that the energy of the pendulum system has limit cycle when there is energy supplement, and prove that there is a unique stable limit cycle in the general pendulum model combined with the theorem of ring domain. Finally, based on the existence of limit cycles of piecewise linear systems with parameters, this paper studies a class of piecewise nonlinear systems with parameters. When the parameters change from 0 to less than 0, the equilibrium point of the system moves from node to focus. The condition and proof of the limit cycle of the system.
【学位授予单位】：江苏大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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