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An improved q-deformed logistic map and its implications

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Abstract

In this paper, we show that the q-deformation scheme applied on both sides of the difference equation of the logistic map is topologically conjugate to the canonical logistic map and therefore there is no dynamical changes by this q-deformation. We propose a correction on this q-deformation scheme and apply it on the logistic map to describe the dynamical changes. We illustrate the Parrondo’s paradox by assuming chaotic region as the gain. Further, we compute the topological entropy in the parameter plane and show the existence of Li-Yorke chaos. Finally, we show that in the neighbourhood of a particular parameter value, q-logistic map has stochastically stable chaos.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Jodhpur, Karwar, 342 037, India

    Divya Gupta & V V M S Chandramouli

Authors
  1. Divya Gupta
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  2. V V M S Chandramouli
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Correspondence to Divya Gupta.

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Gupta, D., Chandramouli, V.V.M.S. An improved q-deformed logistic map and its implications. Pramana - J Phys 95, 175 (2021). https://doi.org/10.1007/s12043-021-02209-7

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  • DOI: https://doi.org/10.1007/s12043-021-02209-7

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