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

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

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

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Vaibhav Varshney

https://orcid.org/0000-0003-2030-7950

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

E-mail Address: vaibhav.varshney1991@gmail.com

Corresponding author.

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Suresh Kumarasamy

https://orcid.org/0000-0001-5618-2278

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

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Manish Dev Shrimali

https://orcid.org/0000-0003-1633-469X

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

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, and

Awadhesh Prasad

https://orcid.org/0000-0003-0123-5146

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

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https://doi.org/10.1142/S0218127424300167Cited by:0 (Source: Crossref)

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.

Keywords:

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