An analytic study of the Vaidyanathan chaotic dynamics in Lorentzian metric which has no similar dynamics in Riemannian metric Online publication date: Mon, 23-Sep-2019
by Najmeh Khajoei; MohammadReza Molaei
International Journal of Modelling, Identification and Control (IJMIC), Vol. 32, No. 2, 2019
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.
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