Limitation of Perpetual Points for Confirming Conservation in Dynamical Systems


Sajad Jafari and Fahimeh Nazarimehr
Biomedical Engineering Department,
Amirkabir University of Technology,
Tehran 15875-4413, Iran
sajadjafari@aut.ac.ir

J. C. Sprott
Department of Physics, University of Wisconsin,
Madison, WI 53706, USA

Sayed Mohammad Reza Hashemi Golpayegani
Biomedical Engineering Department,
Amirkabir University of Technology,
Tehran 15875-4413, Iran

Received May 23, 2015

ABSTRACT
Perpetual Points (PPs) have been introduced as an interesting new topic in nonlinear dynamics, and there is a hypothesis that these points can determine whether a system is dissipative or not. This paper demonstrates that this hypothesis is not true since there are counterexamples. Furthermore, we explain that it is impossible to determine dissipation of a system based only on the structure of the system and its equations.

Ref: S. Jafari, F. Nazarimehr, J. C. Sprott, and S. M. R. H. Golpayegani, International Journal of Bifurcation and Chaos 25 1550182 (2015)

The complete paper is available in PDF format.

Return to Sprott's Books and Publications.