Non-existence of Shilnikov chaos in continuous-time systems

Z. ELHADJ;J.C.SPROTT

doi:10.1007/s10483-012-1556-7

Applied Mathematics and Mechanics >

2012 , Vol. 33 >Issue 3: 371 - 374

DOI: https://doi.org/10.1007/s10483-012-1556-7

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Non-existence of Shilnikov chaos in continuous-time systems

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Received date: 2011-03-03

Revised date: 2011-11-28

Online published: 2012-03-01

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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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Z. ELHADJ;J.C.SPROTT . Non-existence of Shilnikov chaos in continuous-time systems[J]. Applied Mathematics and Mechanics, 2012 , 33(3) : 371 -374 . DOI: 10.1007/s10483-012-1556-7

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