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Existence of multistability in the dynamical behavior of q-deformed Lozi map

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Abstract

Dynamics, bifurcations, strange attractors, and related nonlinear phenomena have been investigated in numerous one and two-dimensional maps. The maps could be smooth, non-differentiable, or even discontinuous. Various deformations of these systems could yield valuable insight into the dynamics of these maps. The quantum deformation or q-deformation of nonlinear maps has been investigated recently in this context. It leads to large excursions in the phase space, and the nature of attractors is very different from those usually observed. We investigate the q-deformed Lozi map. The q-deformation of either variable or both variables is studied from the viewpoint of bifurcations, possible multistability, and the nature of attractors. A rich structure of basins of coexisting attractors for various strengths of q-deformation is investigated. The initial conditions that lead to unbounded trajectories in the absence of q-deformation may get confined for slight q-deformation. Chaotic synchronization of two coupled q-deformed Lozi maps is observed, and an analytic criterion has been given for the same.

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Acknowledgements

P. M. Gade and D. D. Joshi thank the DST-SERB (CRG/2020/003993) for financial assistance.

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Author notes

  1. Pratik M. Gaiki, Priyanka D. Bhoyar and Divya D. Joshi have contributed equally to this work.

Authors and Affiliations

  1. Department of Physics, Shri Shivaji Education Society Amravati’s, Shri Shivaji Arts, Commerce and Science College, Motala, Dist. Buldhana, Maharashtra, 443103, India

    Pratik M. Gaiki

  2. Department of Physics, Seth Kesarimal Porwal College of Arts and Science and Commerce, Kamptee, Nagpur, Maharashtra, 444101, India

    Priyanka D. Bhoyar

  3. Department of Physics, R.T.M. Nagpur University, Nagpur, Maharashtra, 440033, India

    Divya D. Joshi & Prashant M. Gade

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  1. Pratik M. Gaiki
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  2. Priyanka D. Bhoyar
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  3. Divya D. Joshi
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  4. Prashant M. Gade
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Correspondence to Priyanka D. Bhoyar.

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Gaiki, P.M., Bhoyar, P.D., Joshi, D.D. et al. Existence of multistability in the dynamical behavior of q-deformed Lozi map. Indian J Phys (2024). https://doi.org/10.1007/s12648-024-03135-1

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