时间延迟下FitzHugh-Nagumo振子的动力学行为与同步研究  

DYNAMIC BEHAVIOR AND SYNCHRONIZATION STUDY IN FITZHUGH-NAGUMO OSCILLATORS UNDER TIME DELAYS

作　　者：于蓉蓉[1] 惠小健[1] 尚云艳[1] YU RongRong;XI XiaoJian;Shang YunYan(Shool of Science,Xijing University,Xi’an 710123,China)

机构地区：[1]西京学院理学院,西安710123

出　　处：《机械强度》2021年第3期517-522,共6页Journal of Mechanical Strength

基　　金：国家自然科学基金项目(11672219);陕西省教育厅计划项目(20JK0965);陕西省自然科学基础研究计划项目(2020JM-646,2021JQ-868)资助。

摘　　要：针对时间延迟下耦合Fitz Hugh-Nagumo振子表现出的混合模式振荡与同步行为,采用Matlab软件和非线性动力学的分析方法,考察不同时间延迟与耦合强度对系统同步行为的影响。首先,在单个时间延迟下研究两个相同耦合FHN阵子的动力学行为,得出系统受时间延迟的大小影响出现了小振荡同相与大振荡失相的现象;随着耦合强度的增加,在更小的参数范围内,系统表现出的振荡模式类型更为复杂。其次,两个时间延迟下FHN阵子受耦合强度大小影响,在不同耦合强度下得出的时间序列中,观察到系统产生的大振幅振荡表现出在同相与失相之间不规则的切换。结论表明,虽然研究的动力系统是简单的,但是表现出的动力学行为出现了同相与失相现象,所观察到的现象与已有的实验模型有着相似之处。In order to study mixed-mode oscillations and synchronization shown by coupled Fitz Hugh-Nagumo oscillators under time delays,the influence of different time delays and coupling strengths on synchronization behavior of the system was investigated by using analysis method of nonlinear dynamics and MATLAB software. Firstly,according to the dynamics of two FHN oscillations coupled by a single time delay,there was small in-phase and large out-of-phase oscillations influenced by diverse time delays. More complex types of mixed-mode oscillations with varying coupling strength were displayed in a smaller range of parameters. Secondly,the dynamics of coupled FHN oscillations affected by the coupling strengths with two time delays was analyzed. The large amplitude oscillations in time series under different coupling strengths could irregularly switch between in phase or out of phase. The results indicate that the considered dynamical system is simple,but there is the phenomenon of inphase and out-of-phase dynamics. The observed phenomena show some similarities to the experimental model studied.

关 键 词：时间延迟 耦合强度 分岔 混合模式振荡 同步 

分 类 号：O313[理学—一般力学与力学基础]