Confirmation of persistent chaos in high dimensions

Zeraoulia Elhadj and J. C. Sprott

Communicated by Jose Luis Lopez-Bonilla


In this letter, we prove rigorously the persistence property of chaos in high dimensions stated as a conjecture in [1]. The idea of the proof is based on a simple remark on the form of the variation of bifurcation parameters. The relevance of this result is that persistent chaos in high dimensions was observed and tested numerically, but without any rigorous proof. Also, this proof shows that persistent chaos still occurs in typical nonlinear high-dimensional dynamical systems such as randomly sampled high-dimensional vector fields (ODEs) or maps.

Ref: E. Zeraoulia and  J. C. Sprott, Palestine Journal of Mathematics 3, 126-128 (2014)

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