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Chen Zhangyao, Chen Yaguang, Bi Qinsheng. BURSTING OSCILLATIONS AS WELL AS THE BIFURCATION MECHANISM INDUCED BY FAST SUBSYSTEM WITH MULTIPLE BALANCES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(4): 699-706. DOI: 10.6052/0459-1879-14-353
Citation: Chen Zhangyao, Chen Yaguang, Bi Qinsheng. BURSTING OSCILLATIONS AS WELL AS THE BIFURCATION MECHANISM INDUCED BY FAST SUBSYSTEM WITH MULTIPLE BALANCES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(4): 699-706. DOI: 10.6052/0459-1879-14-353
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BURSTING OSCILLATIONS AS WELL AS THE BIFURCATION MECHANISM INDUCED BY FAST SUBSYSTEM WITH MULTIPLE BALANCES

  • Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, China

Funds: The project was supported by the National Natural Science Foundation of China (20976075, 11472115, 11302136, 11472116) and the Scientific and Technological Foundation of Zhenjiang, China (GY2013032, GY2013052).
  • Received Date: November 15, 2014
  • Revised Date: April 19, 2015
    Graphical Abstract
    • Abstract
  • By introducing subcircuit module and taking suitable values for the parameters as well as the characteristics of the nonlinear resistance, a four-dimensional generalized Hartley model whose fast subsystem has multiple balances is established. Based on the multiple balances as well as stabilities of the fast subsystem, bifurcation sets are derived, which divide the parameter space into different regions. In each region, nonlinear dynamical behaviors as well as the bifurcation patterns corresponding to different critical conditions are obtained. Two typical cases with different bifurcations are investigated, in which two different bursting oscillations with multiple balances of the fast subsystem involved are presented. Combining with the bifurcation analysis of the fast subsystem, the mechanism of the alternation between quiescent state and the spiking state is explored, which reveals that multiple balances of the fast subsystem not only may cause multiple quiescent states and spiking states to involve a periodic burster simultaneously, but also may lead to the multiplicity of patterns of bursting oscillations.
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    • References (20)
  • Theodosiou C, Sikelis K, Natsiavas S. Periodic steady state response of large scale mechanical models with local nonlinearities. Int J Solids Struct, 2009, 46(20): 3565-3576
    Bi QS. The mechanism of bursting phenomena in Belousov-Zhabotinsky(BZ) chemical reaction with multiple time scale. Sci China-Technol Sci, 2010, 53(3): 748-760
    Yang ZQ, Lu QS, Li L. The genesis of period-adding bursting without bursting-chaos in the Chay model. Chaos Solitons Fractals, 2006, 27(3): 689-697
    Wang HX, Lu QS, Wang QY. Bursting and synchronization transition in the coupled modified ML neurons. Commun Nonlinear Sci, 2008, 13(8): 1668-1675
    陈章耀, 张晓芳, 毕勤胜. 周期激励下Hartley模型的簇发及其分岔机制. 力学学报, 2010, 42(4): 765-773 (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))
    Abobda LT, Woafo P. Subharmonic and bursting oscillations of a ferromagnetic mass fixed on a spring and subjected to an AC electromagnet. Communications in Nonlinear Science and Numerical Simulation, 2012, 17(7): 3082-3091
    张正娣, 毕勤胜. 自激作用下洛伦兹振子的簇发现象及其分岔机制. 中国科学: 物理学力学天文学, 2013, 43(4): 511-517 ( Zhang Zhendi, Bi Qinsheng. Bursting phenomenon as well as the bifurcation mechanism of self-excited Lorenz system. Sci Sin-Phys Mech Astron, 2013, 43(4): 511-517 (in Chinese))
    Wang HX, Wang QY, Lu QS. Bursting oscillations, bifurcation and synchronization in neuronal systems. Chaos Solitons Fractals, 2011, 44(8): 667-675
    陈章耀, 毕勤胜. 非线性电路的簇发现象及其分岔机制. 控制理论与应用, 2011, 28(10): 1413-1420 (Chen Zhangyao, Bi Qinsheng. Bursting phenomena as well as bifurcation mechanism in nonlinear circuit. Control Theory & Applications, 2011, 28(10): 1413-1420 (in Chinese))
    Shen JH, Zhou ZY. Fast-slow dynamics in logistic models with slowly varying parameters. Commun Nonlinear Sci Numer Simul, 2013, 18(8): 2213-2221
    Perc M, Marhl M. Different types of bursting calcium oscillations in non-excitable cells. Chaos Solitons and Fractals, 2003, 18(4): 759-773
    Simo H, Woafo P. Bursting oscillations in electromechanical systems. Mechanics Research Communications. 2011, 38(8): 537-547
    Han XJ, Jiang B, Bi QS. Symmetric bursting of focus-focus type in the controlled Lorenz system with two time scales. Physics Letters A, 2009, 373(40): 3643-3649
    Bi QS, Zhang ZD. Bursting phenomena as well as the bifurcation mechanism in controlled Lorenz oscillation with two scales. Physics Letters A, 2011, 375(8): 1183-1190
    杨卓琴, 张璇. 3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): 1705081-1705088 (Yan Zhuoqin, Zhang Xuan. Compound bursting in an electrical coupling model with three different time scales. Acta Phys Sin, 2013, 62(17): 1705081-1705088 (in Chinese))
    Kingni ST, Keuninckx L, Woafo P, et al. Dissipative chaos, Shilnikov chaos and bursting oscillations in a three-dimensional autonomous system: theory and electronic implementation. Nonlinear Dynamics, 2013, 73(1-2): 1111-1123
    Hartley TT, Monssayebi F. Matrix integrators for real-time simulation of singular systems. In: Proc of Amer Control Conf, Ptiisburgh, USA, 1989. 419-423
    Kuzenetsov YA. Elements of Applied Bifurcation Theory. 2nd ed, New York: Springer-Verlag, 1998. 265-277
    陈予恕. 非线性振动系统的分岔和混沌理论. 北京: 高等教育出版社, 1993
    Han XJ, Bi QS. Bursting oscillations in Duffing's equation with slowly changing external forcing. Commun Nonlinear Sci Numer Simul, 2011, 16(8): 4146-4152
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