Role of UPOs in Characterizing the Hidden Attractors: A Comparison with Self-Excited Attractors-Reference-Cited by-同舟云学术

Role of UPOs in Characterizing the Hidden Attractors: A Comparison with Self-Excited Attractors

Published:2024-06-15 Issue:08 Volume:34 Page:
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Bhindwar Medha¹²^ORCID,Varshney Vaibhav³^ORCID,Kumarasamy Suresh⁴^ORCID,Shrimali Manish Dev⁵^ORCID,Prasad Awadhesh¹^ORCID

Affiliation:

1. Department of Physics and Astrophysics, University of Delhi, New Delhi 110007, Delhi NCT, India

2. School of Physics, Indian Institute of Science Education and Research Thiruvananthapuram, Thiruvananthapuram 695551, Kerala, India

3. Department of Physics, Dyal Singh College, University of Delhi, New Delhi 110003, Delhi NCT, India

4. Center for Computational Modeling, Chennai Institute of Technology, Chennai 600069, Tamil Nadu, India

5. Department of Physics, Central University of Rajasthan, Ajmer 305817, Rajasthan, India

Abstract

In this paper, we detect Unstable Periodic Orbits (UPOs) of both self-excited and hidden attractors using the Damped Newton–Raphson–Mees algorithm. This study answers one of the long-standing questions about the size of a hidden attractor. We observe that the UPOs of the self-excited attractor are spread in a thick region within the phase space at varying distances from the fixed point, whereas the UPOs of hidden attractors are confined to a thin layer. This reveals details concerning the size of a hidden attractor. We demonstrate this for a hidden attractor without a fixed point and for a hidden attractor with a single stable fixed point. To compare the results with self-excited attractors, we have taken Lorenz and Rössler attractor as examples.

Funder

Center for Computational Modeling, Chennai Institute of Technology (CIT), India

Publisher

World Scientific Pub Co Pte Ltd

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127424300167

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