Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (3): 371-374.doi: https://doi.org/10.1007/s10483-012-1556-7
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Z. ELHADJ1, J.C.SPROTT2
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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.
2010 MSC Number:
65P20
Z. ELHADJ;J.C.SPROTT. Non-existence of Shilnikov chaos in continuous-time systems. Applied Mathematics and Mechanics (English Edition), 2012, 33(3): 371-374.
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URL: https://www.amm.shu.edu.cn/EN/10.1007/s10483-012-1556-7
https://www.amm.shu.edu.cn/EN/Y2012/V33/I3/371
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