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Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (3): 371-374.doi: https://doi.org/10.1007/s10483-012-1556-7

• 论文 • 上一篇    下一篇

Non-existence of Shilnikov chaos in continuous-time systems

 Z. ELHADJ1, J.C.SPROTT2   

  • 收稿日期:2011-03-03 修回日期:2011-11-28 出版日期:2012-03-02 发布日期:2012-03-01

Non-existence of Shilnikov chaos in continuous-time systems

 Z. ELHADJ1, J.C.SPROTT2   

  • Received:2011-03-03 Revised:2011-11-28 Online:2012-03-02 Published:2012-03-01

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764

被引次数

8

摘要： In this paper, a non-existence condition for homoclinic and heteroclinic orbits in n-dimensional, continuous-time, and smooth systems is obtained. Based on this result and an elementary example, it can be conjectured that there is a fourth kind of chaos in polynomial ordinary differential equation (ODE) systems characterized by the nonexistence of homoclinic and heteroclinic orbits.

Abstract: In this paper, a non-existence condition for homoclinic and heteroclinic orbits in n-dimensional, continuous-time, and smooth systems is obtained. Based on this result and an elementary example, it can be conjectured that there is a fourth kind of chaos in polynomial ordinary differential equation (ODE) systems characterized by the nonexistence of homoclinic and heteroclinic orbits.

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