On the Non-Existence of Shilnikov Chaos in Continuous-Time Systems

Zeraoulia Elhadj; J.C.Sprott

doi:10.3879/j.issn.1000-0887.2012.03.008

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Zeraoulia Elhadj, J.C.Sprott. On the Non-Existence of Shilnikov Chaos in Continuous-Time Systems[J]. Applied Mathematics and Mechanics, 2012, 33(3): 353-356. doi: 10.3879/j.issn.1000-0887.2012.03.008

Citation:

Zeraoulia Elhadj, J.C.Sprott. On the Non-Existence of Shilnikov Chaos in Continuous-Time Systems[J]. Applied Mathematics and Mechanics, 2012, 33(3): 353-356. doi: 10.3879/j.issn.1000-0887.2012.03.008

Citation:

Zeraoulia Elhadj, J.C.Sprott. On the Non-Existence of Shilnikov Chaos in Continuous-Time Systems[J]. Applied Mathematics and Mechanics, 2012, 33(3): 353-356. doi: 10.3879/j.issn.1000-0887.2012.03.008

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On the Non-Existence of Shilnikov Chaos in Continuous-Time Systems

doi: 10.3879/j.issn.1000-0887.2012.03.008

Zeraoulia Elhadj¹,
J.C.Sprott²

¹Department of Mathematics, University of Tebessa, 12002, Algeria;²Department of Physics, University of Wisconsin, Madison, WI 53706, USA

Received Date: 2011-03-07
Rev Recd Date: 2011-11-25
Publish Date: 2012-03-15

Abstract

Abstract

A non-existence condition for homoclinic and heteroclinic orbits in n-dimensional, continuous-time, smooth systems was obtained. Based on this result, and using an elementary example, it was conjectured that there was a fourth kind of chaos in polynomial ODE systems characterized by the nonexistence of homoclinic and heteroclinic orbits.
- homoclinic chaos,
- heteroclinic chaos,
- non-existence of Shilnikov chaos

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References(14)

References

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