搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

多平衡态下簇发振荡产生机理及吸引子结构分析

邢雅清 陈小可 张正娣 毕勤胜

引用本文:
Citation:

多平衡态下簇发振荡产生机理及吸引子结构分析

邢雅清, 陈小可, 张正娣, 毕勤胜

Mechanism of bursting oscillations with multiple equilibrium states and the analysis of the structures of the attractors

Xing Ya-Qing, Chen Xiao-Ke, Zhang Zheng-Di, Bi Qin-Sheng
PDF
导出引用
  • 以周期激励下受控Lorenz模型为例, 考察了多平衡态共存下激励频率与系统固有频率之间存在量级差距也即存在频域上的不同尺度时的耦合效应. 由于激励频率远小于系统的固有频率, 因此将整个激励项视为慢变参数, 分析随慢变参数变化下的各种分岔模式及其相应的分岔行为, 指出在一定条件下, 不同平衡点会产生Hopf分岔和fold分岔. 根据分岔条件的不同, 给出了两种典型情况下的簇发振荡, 并通过引入转换相图, 揭示了不同簇发的产生机理, 指出多平衡态和多种分岔共存不仅会导致沉寂态和激发态的多样性, 而且会使得不同沉寂态和激发态之间存在着不同的转换形式.
    The main purpose of this article is to explore the bursting behaviors as well as the mechanism when multiple equilibrium states evolve into the bursting attractors. Taking the controlled Lorenz model with periodic excitation for example, the coupling effect of different scales in frequency domain corresponding to the case that an order gap exists between the exciting frequency and the natural frequency of the system with multiple equilibrium states is investigated. Unlike the autonomous slow-fast coupling system, neither obvious slow nor fast subsystems can be observed in a periodically excited system. Since the exciting frequency is far less than the natural frequency of the system, the whole exciting term can be considered as a slow-varying parameter, leading to the generalized autonomous system. With the variation of the slowly-varying parameter, the bifurcation forms as well as the behaviors for different equilibrium states in the generalized autonomous system are explored. It is pointed out that for certain conditions, Hopf bifurcation and fold bifurcations related to different equilibrium points can be observed. According to the conditions related to different bifurcations, the bursting oscillations in two typical cases are presented. In order to explore the mechanism of bursting oscillation, transformed phase portraits are introduced in which the whole exciting term is treated as a generalized state variable so that the relationship between the original state variables and the slow-varying parameter can be clearly described. By employing the transformed phase portraits, the bifurcation mechanisms of different bursting attractors are presented. For the conditions where only fold bifurcation exists between two equilibrium states in the generalized autonomous system, two un-symmetric bursting attractors can be observed. With the variation of parameters, when the repetitive spiking oscillations pass across the attracting basin of another equilibrium states, the two bursting attractors interact with each other to form an enlarged symmetric bursting attractor. For the conditions where both the Hopf and fold bifurcations evolve into the bursting attractors, multiple quiescent states as well as repetitive spiking states exist in the bursting oscillations, which may lead to complicated behaviors. It is found that the coexistence of multiple equilibrium states as well as the related bifurcation forms not only leads to multiple forms of quiescent states and the spiking states, but also results in different switching forms between different quiescent states and the spiking states.
      通信作者: 毕勤胜, qbi@mail.ujs.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 21276115, 11472115, 11472116)资助的课题.
      Corresponding author: Bi Qin-Sheng, qbi@mail.ujs.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 21276115, 11472115, 11472116).
    [1]

    Lashina E A, Chumakova N A, Chumakov G A, Boronin A I 2009 Chem. Eng. J. 154 82

    [2]

    Qin L, Liu F C, Liang L H, Hou T T 2014 Acta Phys. Sin. 63 090502 (in Chinese) [秦利, 刘福才, 梁利环, 侯甜甜 2014 物理学报 63 090502]

    [3]

    Li X H, Bi Q S 2012 Acta Phys. Sin. 61 020504 (in Chinese) [李向红, 毕勤胜 2012 物理学报 61 020504]

    [4]

    Zhu Y P, Tu S, Luo Z H 2012 Chem. Eng. Res. Des. 90 1361

    [5]

    Cai Z Q, Li X F, Zhou H 2015 Aerosp. Sci. Technol. 42 384

    [6]

    Wang H X, Wang Q Y, Lu Q S 2011 Chaos Soliton. Fract. 44 667

    [7]

    Ferrari F A S, Viana R L, Lopes S R, Stoop R 2015 Neural Networks 66 107

    [8]

    Huang X G, Xu J X, He D H, Xia J L, L Z J 1999 Acta Phys. Sin. 48 1810 (in Chinese) [黄显高, 徐健学, 何岱海, 夏军利, 吕泽均 1999 物理学报 48 1810]

    [9]

    Izhikevich E M 2000 Int. J. Bifur. Chaos 10 1171

    [10]

    Ma J, Jin W Y, Song X L 2015 Chin. Phys. B 24 0128710

    [11]

    Bi Q S, Li X H 2013 Chin. Phys. B 22 040504

    [12]

    Zhang Y, Bi Q S 2011 Chin. Phys. B 20 010504

    [13]

    Chumakov G A, Chumakova N A 2003 Chem. Engineer. J. 91 151

    [14]

    Shilnikov A, Kolomiets M 2008 Int. J. Bifurcat. Chaos 18 2141

    [15]

    Kiss I Z, Pelster L N, Wickramasinghe M, Yablonsky G S 2009 Phys. Chem. 11 5720

    [16]

    Kingni S T, Nana B, Mbouna Ngueuteu G S, Woafo P, Danckaert J 2014 Chaos Soliton. Fract. 71 29

    [17]

    Yang Z Q, Lu Q S 2006 Chin. Phys. B 15 0514

    [18]

    Yu H T, Wang J, Deng B, Wei X L 2013 Chin. Phys. B 22 018701

    [19]

    Izhikevich E M, Desai N S, Walcott E C, Hoppensteadt F C 2003 Trends Neurosci. 26 161

  • [1]

    Lashina E A, Chumakova N A, Chumakov G A, Boronin A I 2009 Chem. Eng. J. 154 82

    [2]

    Qin L, Liu F C, Liang L H, Hou T T 2014 Acta Phys. Sin. 63 090502 (in Chinese) [秦利, 刘福才, 梁利环, 侯甜甜 2014 物理学报 63 090502]

    [3]

    Li X H, Bi Q S 2012 Acta Phys. Sin. 61 020504 (in Chinese) [李向红, 毕勤胜 2012 物理学报 61 020504]

    [4]

    Zhu Y P, Tu S, Luo Z H 2012 Chem. Eng. Res. Des. 90 1361

    [5]

    Cai Z Q, Li X F, Zhou H 2015 Aerosp. Sci. Technol. 42 384

    [6]

    Wang H X, Wang Q Y, Lu Q S 2011 Chaos Soliton. Fract. 44 667

    [7]

    Ferrari F A S, Viana R L, Lopes S R, Stoop R 2015 Neural Networks 66 107

    [8]

    Huang X G, Xu J X, He D H, Xia J L, L Z J 1999 Acta Phys. Sin. 48 1810 (in Chinese) [黄显高, 徐健学, 何岱海, 夏军利, 吕泽均 1999 物理学报 48 1810]

    [9]

    Izhikevich E M 2000 Int. J. Bifur. Chaos 10 1171

    [10]

    Ma J, Jin W Y, Song X L 2015 Chin. Phys. B 24 0128710

    [11]

    Bi Q S, Li X H 2013 Chin. Phys. B 22 040504

    [12]

    Zhang Y, Bi Q S 2011 Chin. Phys. B 20 010504

    [13]

    Chumakov G A, Chumakova N A 2003 Chem. Engineer. J. 91 151

    [14]

    Shilnikov A, Kolomiets M 2008 Int. J. Bifurcat. Chaos 18 2141

    [15]

    Kiss I Z, Pelster L N, Wickramasinghe M, Yablonsky G S 2009 Phys. Chem. 11 5720

    [16]

    Kingni S T, Nana B, Mbouna Ngueuteu G S, Woafo P, Danckaert J 2014 Chaos Soliton. Fract. 71 29

    [17]

    Yang Z Q, Lu Q S 2006 Chin. Phys. B 15 0514

    [18]

    Yu H T, Wang J, Deng B, Wei X L 2013 Chin. Phys. B 22 018701

    [19]

    Izhikevich E M, Desai N S, Walcott E C, Hoppensteadt F C 2003 Trends Neurosci. 26 161

  • [1] 宋锦, 魏梦可, 姜文安, 张晓芳, 韩修静, 毕勤胜. 经由脉冲式爆炸连接的复合式张弛振荡. 物理学报, 2020, 69(7): 070501. doi: 10.7498/aps.69.20191812
    [2] 张绍华, 王聪, 张宏立. 永磁同步电动机的簇发振荡分析及协同控制. 物理学报, 2020, 69(21): 210501. doi: 10.7498/aps.69.20200413
    [3] 张正娣, 刘亚楠, 李静, 毕勤胜. 分段Filippov系统的簇发振荡及擦边运动机理. 物理学报, 2018, 67(11): 110501. doi: 10.7498/aps.67.20172421
    [4] 张正娣, 刘杨, 张苏珍, 毕勤胜. 余维-1非光滑分岔下的簇发振荡及其机理. 物理学报, 2017, 66(2): 020501. doi: 10.7498/aps.66.020501
    [5] 吴天一, 陈小可, 张正娣, 张晓芳, 毕勤胜. 非对称型簇发振荡吸引子结构及其机理分析. 物理学报, 2017, 66(11): 110501. doi: 10.7498/aps.66.110501
    [6] 高超, 毕勤胜, 张正娣. 一个跃变电路切换系统的振荡行为及分岔机理分析. 物理学报, 2013, 62(2): 020504. doi: 10.7498/aps.62.020504
    [7] 杨卓琴, 张璇. 三个不同时间尺度的电耦合模型的组合簇放电. 物理学报, 2013, 62(17): 170508. doi: 10.7498/aps.62.170508
    [8] 李旭, 张正娣, 毕勤胜. 两时间尺度下非光滑广义蔡氏电路系统的簇发振荡机理. 物理学报, 2013, 62(22): 220502. doi: 10.7498/aps.62.220502
    [9] 姜海波, 李涛, 曾小亮, 张丽萍. 周期脉冲作用下Logistic映射的复杂动力学行为及其分岔分析. 物理学报, 2013, 62(12): 120508. doi: 10.7498/aps.62.120508
    [10] 乔盼盼, 艾合买提·阿不力孜, 蔡江涛, 路俊哲, 麦麦提依明·吐孙, 日比古·买买提明. 利用热平衡态超导电荷量子比特实现量子隐形传态. 物理学报, 2012, 61(24): 240303. doi: 10.7498/aps.61.240303
    [11] 李绍龙, 张正娣, 吴天一, 毕勤胜. 广义BVP电路系统的振荡行为及其非光滑分岔机理. 物理学报, 2012, 61(6): 060504. doi: 10.7498/aps.61.060504
    [12] 吴天一, 张正娣, 毕勤胜. 切换电路系统的振荡行为及其非光滑分岔机理. 物理学报, 2012, 61(7): 070502. doi: 10.7498/aps.61.070502
    [13] 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): 020504. doi: 10.7498/aps.61.020504
    [14] 唐先柱, 彭增辉, 刘永刚, 鲁兴海, 宣丽. 相变前的热力学平衡态对铁电液晶排列的影响. 物理学报, 2010, 59(9): 6261-6265. doi: 10.7498/aps.59.6261
    [15] 陈章耀, 张晓芳, 毕勤胜. 广义Chua电路簇发现象及其分岔机理. 物理学报, 2010, 59(4): 2326-2333. doi: 10.7498/aps.59.2326
    [16] 张开成. Sherrington-Kirkpatric自旋玻璃模型的非平衡态性质. 物理学报, 2009, 58(8): 5673-5678. doi: 10.7498/aps.58.5673
    [17] 王华滔, 秦昭栋, 倪玉山, 张文. 不同晶体取向下纳米压痕的多尺度模拟. 物理学报, 2009, 58(2): 1057-1063. doi: 10.7498/aps.58.1057
    [18] 徐勇, 张世昌. 反向导引磁场自由电子激光中平衡态电子相轨道. 物理学报, 1994, 43(7): 1096-1104. doi: 10.7498/aps.43.1096
    [19] 王昌标. 自由电子激光中平衡态螺旋轨道的稳定性问题. 物理学报, 1992, 41(7): 1092-1096. doi: 10.7498/aps.41.1092
    [20] 冯克安. 非平衡态相变的两例——光学参量振荡和激光. 物理学报, 1978, 27(3): 322-330. doi: 10.7498/aps.27.322
计量
  • 文章访问数:  5259
  • PDF下载量:  434
  • 被引次数: 0
出版历程
  • 收稿日期:  2015-11-23
  • 修回日期:  2016-01-25
  • 刊出日期:  2016-05-05

/

返回文章
返回