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Complex bursting patterns in van der pol system with two slowly changing external forcings

Science China(Technological Sciences) 2012年第3期55卷 702-708页

作者： HAN XiuJing BI QinSheng Faculty of Civil Engineering and Mechanics Jiangsu UniversityZhenjiang 212013China

This paper investigates the generation of complex bursting patterns in van der pol system with two slowly changing external forcings. Complex bursting patterns, including complex periodic bursting and chaotic bursting, are presented for the cases when the two frequencies are commensurate and incommensurate. These complex bursting patterns are novel and have not been reported in previous work. Based on the fast-slow dynamics, the evolution processes of the slow forcing are presented to reveal the dynamical mechanisms undedying the appearance of these complex bursting patterns. With the change of ampli- tudes and frequencies, the slow forcing may visit the spiking and rest areas in different ways, which leads to the generation of different complex bursting patterns.

关键词： van der pol system two external forcings complex periodic bursting patterns chaotic bursting

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Complex bursting patterns in van der pol system with two slowly changing external forcing

Complex bursting patterns in Van der Pol system with two slo...

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第十四届全国非线性振动暨第十一届全国非线性动力学和运动稳定性学术会议

作者： Xiujing Han Qinsheng Bi Faculty of Civil Engineering and Mechanics Jiangsu University

This paper investigates the generation of complex bursting patterns in van der pol system with two slowly changing external *** bursting patterns, including complex periodic bursting and chaotic bursting are presented for the cases when the two frequencies are commensurate and *** complex bursting patterns are novel and have not been reported in previous *** on the

关键词： van der pol system Two external forcing Complex periodic bursting patterns Chaotic bursting

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Approximate analytical solution in slow-fast system based on modified multi-scale method

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Applied Mathematics and Mechanics(English Edition) 2020年第4期41卷 605-622页

作者： Xianghong LI Jianhua TANG Yanli WANG Yongjun SHEN Department of Mathematics and Physics Shijiazhuang Tiedao UniversityShijiazhuang 050043China Department of Mechanical Engineering Shijiazhuang Tiedao UniversityShijiazhuang 050043China

A simple,yet accurate modi?ed multi-scale method(MMSM)for an approximately analytical solution in nonlinear oscillators with two time scales under forced harmonic excitation is *** method depends on the classical multi-scale method(MSM)and the method of variation of *** that the forced excitation is a constant,one could easily obtain the approximate analytical solution of the simpli?ed system based on the traditional ***,this solution for the oscillator under forced harmonic excitation could be established after replacing the harmonic excitation by the constant *** certify the correctness and precision of the proposed analytical method,the van der pol system with two scales subject to slowly periodic excitation is investigated;this system presents rich dynamical phenomena such as spiking(SP),spiking-quiescence(SP-QS),and quiescence(QS)*** approximate analytical expressions of the three types of responses are given by the MMSM,and it can be found that the precision of the new analytical method is higher than that of the classical MSM and better than that of the harmonic balance method(HBM).The results obtained by the present method are considerably better than those obtained by traditional methods,quantitatively and qualitatively,particularly when the excitation frequency is far less than the natural frequency of the system.

关键词： modified multi-scale method(MMSM) slow-fast system multi-scale method(MSM) van der pol system

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