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一类混沌系统中的簇发振荡及其延迟叉形分岔行为

郑健康 张晓芳 毕勤胜

郑健康, 张晓芳, 毕勤胜. 一类混沌系统中的簇发振荡及其延迟叉形分岔行为[J]. 力学学报, 2019, 51(2): 540-549. doi: 10.6052/0459-1879-18-241
引用本文: 郑健康, 张晓芳, 毕勤胜. 一类混沌系统中的簇发振荡及其延迟叉形分岔行为[J]. 力学学报, 2019, 51(2): 540-549. doi: 10.6052/0459-1879-18-241
Jiankang Zheng, Xiaofang Zhang, Qinsheng Bi. BURSTING OSCILLATIONS AS WELL AS THE DELAYED PITCHFORK BIFURCATION BEHAVIORS IN A CLASS OF CHAOTIC SYSTEM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(2): 540-549. doi: 10.6052/0459-1879-18-241
Citation: Jiankang Zheng, Xiaofang Zhang, Qinsheng Bi. BURSTING OSCILLATIONS AS WELL AS THE DELAYED PITCHFORK BIFURCATION BEHAVIORS IN A CLASS OF CHAOTIC SYSTEM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(2): 540-549. doi: 10.6052/0459-1879-18-241

一类混沌系统中的簇发振荡及其延迟叉形分岔行为

doi: 10.6052/0459-1879-18-241
基金项目: 国家自然科学基金资助项目(11632008);国家自然科学基金资助项目(11872188)
详细信息
    作者简介:

    2) 张晓芳,副教授,主要研究方向:动力学与控制.E-mail: xfzhang@ujs.edu.cn

  • 中图分类号: O322

BURSTING OSCILLATIONS AS WELL AS THE DELAYED PITCHFORK BIFURCATION BEHAVIORS IN A CLASS OF CHAOTIC SYSTEM

  • 摘要: 由于多时间尺度问题在实际工程系统中广泛存在,关于其复杂动力学行为及其产生机制的研究已成为当前国内外的热点课题之一.簇发振荡是多时间尺度系统复杂动力学行为的典型代表,而分岔延迟又是簇发振荡中的常见现象.本文为探讨非线性系统中分岔延迟所引发的簇发振荡的分岔机制,在一个三维混沌系统中引入参数激励,当激励频率远小于系统的固有频率时,系统产生了两时间尺度簇发振荡.将整个激励项看做慢变参数,激励系统转化为广义自治系统也即快子系统,分析快子系统平衡点的稳定性以及分岔条件,并运用快慢分析法和转换相图揭示了簇发振荡的动力学机理.文中考察了4组参数条件下系统的动力学行为,研究发现当慢变激励项周期性地通过分岔点时,系统产生了明显的超临界叉形分岔延迟行为,随着参数激励振幅的增大,分岔延迟的时间也逐渐延长,当这种延迟的动态行为终止于不同的参数区域时,导致系统轨线围绕不同稳定吸引子(平衡点,极限环)运动,从而得到了不同的簇发振荡行为.

     

  • [1] Li XH, Hou JY, Chen JF . An analytical method for Mathieu oscillator based on method of variation of parameter. Communications in Nonlinear Science & Numerical Simulation, 2016,37:326-353
    [2] Dai HH, Yue XK, Liu C . A multiple scale time domain collocation method for solving nonlinear dynamical system. International Journal of Nonlinear Mechanics, 2014,67:342-351
    [3] 张洪武, 张盛, 毕金英 . 周期性结构热动力时间-空间多尺度分析. 力学学报, 2006,38(2):226-235
    [3] ( Zhang Hongwu, Zhang Sheng, Bi Jinying . Thermodynamic analysis of multiphase periodic structures based on a spatial and temporal multiple scale method. Chinese Journal of Theoretical and Applied Mechanics, 2006,38(2):226-235 (in Chinese))
    [4] Br?ns M, Kaasen R . Canards and mixed-mode oscillations in a forest pest model. Theoretical Population Biology, 2010,77(4):238-242
    [5] 古华光 . 神经系统信息处理和异常功能的复杂动力学. 力学学报, 2017,49(2):410-420
    [5] ( Gu Guaguang . Complex dynamics of the nervous system for information processing and abnormal functions. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(2):410-420 (in Chinese))
    [6] Liu X, Huo B . Nonlinear vibration and multimodal interaction analysis of transmission line with thin ice accretions. International Journal of Applied Mechanics, 2015,7(1):1540007
    [7] Li XH, Bi QS . Single-Hopf bursting in periodic perturbed Belousov-Zhab-otinsky reaction with two time scales. Chin. phys. lett, 2013,30(1):10503-10506
    [8] 李向红, 毕勤胜 . 铂族金属氧化过程中的簇发振荡及其诱发机理. 物理学报, 2012,61(2):88-96
    [8] ( Li Xianghong, Bi Qinsheng . Bursting oscillations and the bifurcation mechanism in oxidation on platinum group metals. Acta Phys Sin, 2012,61(2):88-96(in Chinese))
    [9] Courbage M, Nekorkin VI, Vdovin LV . Chaotic oscillations in a map-based model of neural activity. Chaos, 2007,17(4):043109
    [10] Izhikevich EM . Resonance and selective communication via bursts in neurons having subthreshold oscillations. Bio Systems, 2002,67(1-3):95-102
    [11] Ferrari FAS, Viana RL, Lopes SR , et al. Phase synchronization of coupled bursting neurons and the generalized Kuramoto model. Neural Networks , 2015,66:107-118
    [12] Bi QS . The mechanism of bursting phenomena in BZ chemical reaction with multiple time scales. Science in China, 2012,10:2820-2830
    [13] 陈章耀, 张晓芳, 毕勤胜 . 周期激励下Hartley模型的簇发及分岔机. 力学学报, 2010,42(4):765-773
    [13] ( Chen Zhangyao, Zhang Xiaofang, Bi Qinsheng . Bursting phenomena as well as the bifurcation mechanism in periodically excited Hartley model. Chinese Journal of Theoretical and Applied Mechanics, 2010,42(4):765-773(in Chinese))
    [14] Farazmand M, Sapsis T . Dynamical indicators for the prediction of bursting phenomena in high-dimensional systems. Physical Review E, 2016,94(3):032212
    [15] Wu H, Bao BC, Liu Z , et al. Chaotic and periodic bursting phenomena in a memristive Wien-bridge oscillator. Nonlinear Dynamics, 2016,83(1-2):893-903
    [16] Fujimoto K, Kaneko K . How fast elements can affect slow dynamics. Physica D , 2003,180(1):1-16
    [17] Egghea L, Rousseaub R . Lorenz theory of symmetric relative concentration and similarity, incorporating variable array length. Mathematical & Computer Modelling, 2006,44(7):628-639
    [18] Stork W . Subharmonic response and synchronisation for the forced van der Pol equation via Cesari's method. Journal of Mathematical Analysis & Applications, 1984,102(1):134-148
    [19] Izhikevich EM . Neural excitability, spiking and bursting. International Journal of Bifurcation and Chaos, 2000,10(6):1171-1266
    [20] Bi QS, Li SL, Kurths J , et al. The mechanism of bursting oscillations with different codimensional bifurcations and nonlinear structures. Nonlinear Dynamics, 2016,85(2):1-13
    [21] Han XJ, Bi QS, Ji P , et al. Fast-slow analysis for parametrically and externally excited systems with two slow rationally related excitation frequencies. Physical Review E, 2015,92(1):012911
    [22] Yu Y, Tang HJ, Han XJ , et al. Bursting mechanism in a time-delayed oscillator with slowly varying external forcing. Communications in Nonlinear Science & Numerical Simulation, 2014,19(4):1175-1184
    [23] 张晓芳, 陈小可, 毕勤胜 . 快慢耦合振子的张驰簇发及其非光滑分岔机制. 力学学报, 2012,44(3):576-583
    [23] ( Zhang Xiaofang, Chen Xiaoke, Bi Qinsheng . Relaxation bursting of a fast-slow coupled oscillation as well as the mechanism of non-smooth bifurcation. Chinese Journal of Theoretical and Applied Mechanics, 2012,44(3):576-583(in Chinese))
    [24] Freire JG, Gallas JAC . Stern-Brocot trees in cascades of mixed-mode oscillations and canards in the extended Bonhoeffer-van der Pol and the FitzHugh-Nagumo models of excitable systems. Phys Lett A, 2011,375(7):1097-1103
    [25] Chumakov GA, Chumakova NA . Relaxation oscillations in a kinetic model of catalytic hydrogen oxidation involving a chase on canards. Chemical Engineering Journal, 2003,91(2):151-158
    [26] 韩修静, 江波, 毕勤胜 . 快慢型超混沌Lorenz系统分析. 物理学报, 2009,58(9):6006-6015
    [26] ( Han Xiujing, Jiang Bo, Bi Qinsheng . Analysis of the fast-slow hyperchaotic Lorenz system. Acta Phys Sin, 2009,58(9):6006-6015(in Chinese))
    [27] Hou JY, Li XH, Zuo DW , et al. Bursting and delay behavior in the Belousov-Zhabotinsky reaction with external excitation. European Physical Journal Plus, 2017,132(6):283
    [28] Baer SM, Erneux T, Rinzel J . The slow passage through a Hopf bifurcation: Delay, memory effects, and resonance. Siam Journal on Applied Mathematics, 1989,49(1):55-71
    [29] Hao LJ, Yang ZQ, Lei JZ . Bifurcation analysis of a delay differential equation model associated with the induction of long-term memory. Chaos Solitons & Fractals, 2015,81:162-171
    [30] Mahmoud GM, Arafa AA, Mahmoud EE . Bifurcations and chaos of time delay Lorenz system with dimension 2$n$+1. European Physical Journal Plus, 2017,132(1):461
    [31] 陈振阳, 韩修静, 毕勤胜 . 一类二维非自治离散系统中的复杂簇发振荡结构. 力学学报, 2017,49(1):165-174
    [31] ( Chen Zhenyang, Han Xiujing, Bi Qinsheng . Complex bursting oscillation structures in a two-dimensional non-autonomous discrete system. Chinese Journal of Theoretical and Applied Mechanics, 2017,49(1):165-174(in Chinese))
    [32] Maree GJM . Slow passage through a pitchfork bifurcation. SIAM Journal on Applied Mathematics, 1996,56(3):889-918
    [33] Premraj D, Suresh K, Banerjee T , et al. An experimental study of slow passage through Hopf and pitchfork bifurcations in a parametrically driven nonlinear oscillator. Communications in Nonlinear Science & Numerical Simulation, 2016,37:212-221
    [34] Yu Y, Han XJ, Zhang C , et al. Mixed-mode oscillations in a nonlinear time delay oscillator with time varying parameters. Communications in Nonlinear Science & Numerical Simulation, 2017,47:23-34
    [35] 陈章耀, 王亚茗, 张春 等. 双状态切换下 BVP振子的复杂行为分析. 力学学报, 2016,48(4):953-962
    [35] ( Chen Zhangyao, Wang Yaming, Zhang Chun , et al. Complicated behaviors as well as the mechanism in BVP oscillator with switches related to two states. Chinese Journal of Theoretical and Applied Mechanics, 2016,48(4):953-962(in Chinese))
    [36] Abooee A, Yaghini-Bonabi HA, Jahed-Motlagh MR . Analysis and circuitry realization of a novel three-dimensional chaotic system. Communications in Nonlinear Science & Numerical Simulation, 2013,18(5):1235-1245
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出版历程
  • 收稿日期:  2018-07-20
  • 刊出日期:  2019-03-18

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