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A Note on the Dynamics of the Logistic Family Modified by Fuzzy Numbers

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Abstract

In this paper, we consider a modification of the well-known logistic family using a family of fuzzy numbers. The dynamics of this modified logistic map is studied by computing its topological entropy with a given accuracy. This computation allows us to characterize when the dynamics of the modified family is chaotic. Besides, some attractors that appear in bifurcation diagrams are explained. Finally, we will show that the dynamics induced by the logistic family on the fuzzy numbers need not be complicated at all.

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Funding

This paper is supported by the grant MTM2017-84079-P funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”, by the European Union.

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Authors and Affiliations

  1. Department of Applied Mathematics and Statistics, Technical University of Cartagena, C/Doctor Flemming Sn, 30202, Cartagena, Spain

    J. S. Cánovas

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  1. J. S. Cánovas
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Correspondence to J. S. Cánovas.

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Cánovas, J.S. A Note on the Dynamics of the Logistic Family Modified by Fuzzy Numbers. Acta Math. Appl. Sin. Engl. Ser. 38, 741–752 (2022). https://doi.org/10.1007/s10255-022-1085-5

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  • DOI: https://doi.org/10.1007/s10255-022-1085-5

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