Title: An analytic study of the Vaidyanathan chaotic dynamics in Lorentzian metric which has no similar dynamics in Riemannian metric

Authors: Najmeh Khajoei; MohammadReza Molaei

Addresses: Mahani Mathematical Research Center and Department of Pure Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran; Young Research Society, Shahid Bahonar University of Kerman, Kerman, Iran ' Mahani Mathematical Research Center and Department of Pure Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

Abstract: In this paper we investigate behaviour at infinity of a physical 3-dimensional chaotic system via Poincaré compactification method. This system has been introduced by Vaidyanathan et al. (2017a). We plot the phase portrait of the system for parameters a and b which appear in the nonlinear part of the system. We will see a set of non-isolated singular points at infinity is a hyperbolic set by considering a Lorentzian metric g on R2 and it is not a hyperbolic set in the sense of Riemannian metrics. We compute a first integral for the resulted system and we prove there is at most a generalised rational first integral when one of its parameters is equal to zero.

Keywords: Poincaré compactification; hyperbolic set; Lorentzian metric; first integral; electronic systems.

DOI: 10.1504/IJMIC.2019.102374

International Journal of Modelling, Identification and Control, 2019 Vol.32 No.2, pp.189 - 195

Received: 27 Nov 2018
Accepted: 04 Mar 2019

Published online: 17 Sep 2019 *

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