频域两尺度下一类Filippov系统的非光滑分析  

Non-smooth Analysis of a Class of Filippov Systems with Two Frequency Scales

作　　者：杨秀芳[1] 张正娣[1] 李绍龙[1] 毕勤胜[1] 

机构地区：[1]江苏大学理学院,江苏镇江212013

出　　处：《河南科技大学学报（自然科学版）》2017年第5期65-69,共5页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(11472115;11472116)

摘　　要：借助于含非光滑分界面的耦合Bohoffer-Van der Pol(BVP)电路系统,引入周期慢变的交流电源,构建两频域尺度的Filippov系统。利用微分包含理论,分析了尺度因素与非光滑因素相互作用的机理。当周期激励频率远远小于系统固有频率时,选取适当参数,得到了具有滑动结构的复杂周期簇发振荡,并结合理论分析揭示了滑动结构的产生机制。数值结果与理论分析吻合较好。Based on the coupling Bohoffer-Van der Pol( BVP) circuit system with a non-smooth boundary,a Filippov system with two frequency scales was established by introducing a periodically changed current source. By utilizing the theory of differential inclusions,the mechanism of interaction between scale factor and non-smooth factor was analyzed. Suitable parameter values were selected so that an order gap existed between the driving frequency and the natural frequency. The complex periodic bursting oscillation with a sliding structure and corresponding generation mechanism were obtained according to the theoretical analysis. And numerical results support the theoretical analysis.

关 键 词：Filippov系统 频域两尺度 非光滑 簇发 滑动结构 

分 类 号：O29[理学—应用数学]