摘要
本文研究了阈值控制策略下不同尺度耦合系统的簇发振荡及其机理.以包含周期激励项的HindmarshRose模型为例,当激励频率与系统固有频率存在量级差异时,引入阈值控制策略,建立了频域间存在快慢耦合的Filippov系统.因激励项可以被视为一个慢变参数,我们可以相应地得到一个向量场不连续的广义自治系统,从而分析了系统在不同区域随慢变参数变化的平衡点及相关分岔.特别地,由于系统的非光滑特性,我们也分析了非光滑分岔出现的条件,给出了滑动区域的解析表达式.基于阈值控制策略,研究了三种切换条件下的簇发振荡,指出了非光滑分界面的变化会产生不同的非光滑分岔,进而导致不同滑动现象的发生,表现为不同形式的沉寂态与激发态.通过叠加转换相图与分岔图,簇发机理得以揭示.
The main idea of this paper is to investigate the bursting oscillations as well as their mechanism in the multi-scale coupling system with threshold control strategy. Taking the periodically excited Hindmarsh-Rose model as an example, when there exists orders of magnitude gap between the exciting frequency and the natural frequency, a Filippov-type system with fast-slow coupling in the frequency domain is established based on the threshold control. Since the exciting term can be regarded as a slowvarying parameter, a generalized autonomous system featuring a discontinuous vector field has been obtained. Hence the equilibrium branches as well as the bifurcations of the autonomous system can be analyzed. Particularly, due to the discontinuousness, the conditions for the non-smooth bifurcations are analyzed, and the sliding regions are presented. Based on the threshold control strategy, bursting attractors with three different control thresholds are investigated, from which one can find that the variation of the non-smooth boundary can lead to different non-smooth bifurcations, causing different sliding movements that correspond to different forms of spiking states and quiescent states. By means of overlapping the transformation phase diagram and the bifurcation diagram, the mechanism of those bursting oscillations are revealed.
作者
葛亚威
陈少敏
毕勤胜
GE Yawei;CHEN Shaomin;BI Qinsheng(Faculty of Civil Engineering and Mechanics,Jiangsu University,Zhenjiang 212013,Jiangsu,China)
出处
《力学季刊》
CAS
CSCD
北大核心
2021年第4期641-651,共11页
Chinese Quarterly of Mechanics
基金
国家自然科学基金(11632008)。
作者简介
葛亚威,硕士生.研究方向:非线性动力学.E-mail:2211823007@stmail.ujs.edu.cn;通信作者:毕勤胜,教授.研究方向:动力学与控制.E-mail:qbi@ujs.edu.cn。
