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Technical Brief

On A Comprehensive Topological Analysis of Moore Spiegel attractor

[+] Author and Article Information
Anirban Ray

Dept. of Physics, Gour Mahavidalya, Malda, West Bengal, India
anirban.chaos@gmail.com

Asesh Roy Chowdhury

High Energy Physics Division, Department of Physics, Jadavpur University, Kolkata - 700 032, India
arc.roy@gmail.com

1Corresponding author.

ASME doi:10.1115/1.4037413 History: Received June 18, 2016; Revised July 03, 2017

Abstract

A topological analysis of the attractor associated with the Moore-Spiegel non-linear system is performed, following the basic idea laid down by Gilmore et al\cite{gil}. Starting with the usual fixed point analysis and their stability, we proceed to study in detail the the process of chaotic orbit extraction with the help of close return map. This is then used to construct the symbolic dynamics associated with it, which is helpful in understanding the sequential change taking place inside the attractor. In the next part we show how to characterize the evolution of the attractor from its birth to the crisis by finding out the homoclinic orbit and the corresponding unstable manifold. In the concluding part of the paper we show how all the pertinent information of the attractor can be encoded in the template leading to the explicit realization of linking numbers and the relative rotation rates.In the concluding section we have touched upon a new approach to chaotic dynamics,using the flow curvature manifold to display the relative positioning of the attractor in relation to the fixed points and the nulllines.

Copyright (c) 2017 by ASME
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