Non-existence of Shilnikov Chaos in Continuous-time Systems
and J. C.
Department of Mathematics, University of
Tébessa, (12002), Algeria;
Department of Physics, University of Wisconsin,
Madison, WI 53706, USA
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
non-existence of homoclinic and heteroclinic orbits.
Ref: E. Zeraoulia and J. C. Sprott,
Applied Mathematics and Mechanics (English Edition) 33, 371-374 (2012)
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