Impulsive homoclinic chaos in Van der Pol Jerk system

被引：0
作者：
Ding Y. [1 ,2 ]
Zhang Q. [1 ]
机构：
[1] School of Mechanical Engineering, Tianjin University
[2] School of Sciences, Tianjin University of Science and Technology
来源：
Transactions of Tianjin University | 2010年 / 16卷 / 06期
基金：
中国国家自然科学基金;
关键词：
chaotic system; homoclinic orbit; Silnikov theorem;
D O I：
10.1007/s12209-010-1400-8
中图分类号：
学科分类号：
摘要：
A 3D continuous autonomous chaotic system is reported, which contains a cubic term and six system parameters. Basic dynamic properties of the new Van der Pol Jerk system are studied by means of theoretical analysis and numerical simulation. Based on the Silnikov theorem, the chaotic characterisitics of the dynamic system are discussed. Using Cardano formula and series solution of differential equation, eigenvalue problem and the existence of homoclinic orbit are studied. Furthermore, a rigorous proof for the existence of Silnikov-sense Smale horseshoes chaos is presented and some conditions which lead to the chaos are obtained. The formation mechanism indicates that this chaotic system has impulsive homoclinic chaos, and numerical simulation demonstrates that there is a route to chaos. © 2010 Tianjin University and Springer-Verlag Berlin Heidelberg.
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收藏
页码：457 / 460
页数：3
相关论文
共 15 条
  • [1] Wang X., Chen G., Yu Xinghuo., Anticontrol of chaos in continuous-time systems via time-delay feedback [J], Chaos, 10, 4, pp. 771-779, (2000)
  • [2] Wang X., Chen Guanrong., Chaotification via arbitrarily small feedback control: Theory, method and applications[ J], International Journal of Bifurcation and Chaos, 10, 3, pp. 549-570, (2000)
  • [3] Guckenheimer J., Hoffman K., Weckesser W., The forced-Van der Pol equation I: Slow flow and its bifurcation[J], SIAM Journal on Applied Dynamical Systems, 2, 1, pp. 1-35, (2003)
  • [4] Acho L., Rolon J., Benitez S., A chaotic oscillator using the Van der Pol dynamic immersed into a Jerk system[J], WSEAS Transactions on Circuits and Systems, 3, 1, pp. 198-199, (2004)
  • [5] Benitez S., Acho L., Impulsive synchronization for a new chaotic oscillator, International Journal of Bifurcation and Chaos, 17, 2, pp. 617-623, (2007)
  • [6] Li Z., Chen G., Wolfgand A., Et al., Homoclinic and heteroclinic orbits in a modified Lorenz system[J], Information Sciences, 165, 3-4, pp. 235-245, (2004)
  • [7] Zhang Q., Tian R., Wang Wei., Chaotic properties of mechanically and electrically coupled nonlinear dynamical systems[J], Acta Physica Sinica, 57, 5, pp. 2799-2804, (2008)
  • [8] Zhou T., Chen G., Yang Qigui., Constructing a new chaotic system based on the Silnikov criterion[J], Chaos, Solitons and Fractals, 19, 4, pp. 985-993, (2004)
  • [9] Wang J., Chen Z., Yuan Zhuzhi., A new chaotic system and analysis of its properties[J], Acta Physica Sinica, 55, 8, pp. 3956-3963, (2006)
  • [10] Silnikov L.P., A contribution of the problem of the structure of an extended neighborhood of rough equilibrium state of saddle focus type[J], Math USSR-Shornik, 10, 1, pp. 91-102, (1970)
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