https://doi.org/10.1140/epjb/s10051-024-00780-7
Regular Article - Statistical and Nonlinear Physics
Hidden attractors in fractional-order discrete maps
1
Department of Physics, Dyal Singh College, University of Delhi, 110003, Delhi, India
2
Division of Dynamics, Lodz University of Technology, 90-924, Stefanowskiego 1/15, Lodz, Poland
3
Center for Nonlinear and Complex Networks, SRM Institute of Science and Technology, 600 089, Chennai, Tamil Nadu, India
4
Department of Computational Biology, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, 602105, Thandalam, Chennai, Tamil Nadu, India
5
Center for Artificial Intelligence, Easwari Engineering College, 600089, Chennai, Tamil Nadu, India
Received:
11
December
2023
Accepted:
28
August
2024
Published online:
21
October
2024
This study investigates the hidden dynamics of fractional-order discrete two-dimensional maps, focusing on the generation of hidden attractors and the impact of order on their size and boundaries. Three different nonlinear maps are used, and various measures, such as phase portraits, bifurcation diagrams, and basin of attraction, are presented. This study also observes changes in basin boundaries of hidden attractors with varying order. The rational memristive maps exhibit a well-defined basin of attraction for a broad range of system orders, with multistability and a riddled basin for some orders. The memristive Gauss map also shows well-defined and riddled basins, however, the quadratic chaotic map demonstrates a decreasing basin size and a riddled basin boundary for higher orders of the system.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
