Dynamics and Global Bifurcations in Two Symmetrically Coupled Non-Invertible Maps

Yamina Soula, Hadi Jahanshahi (), Abdullah A. Al-Barakati and Irene Moroz
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Yamina Soula: Department of Mathematics, University of Oum el Bouaghi, Oum El Bouaghi 04000, Algeria
Hadi Jahanshahi: Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB R3T 5V6, Canada
Abdullah A. Al-Barakati: Communication Systems and Networks Research Group, Department of Information Systems, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Irene Moroz: Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK

Mathematics, 2023, vol. 11, issue 6, 1-13

Abstract: The theory of critical curves determines the main characteristics of a discrete dynamical system in two dimensions. One important property that has garnered recent attention is the problem of chaos synchronization, along with the location of its chaotic attractors, basin boundaries, and bifurcation mechanisms. Varying the parameters of the maps reveals the instrumental role that these curves play, where the bifurcation leads to complex topological structures of the basins occurs by contact with the basin boundaries, resulting in the appearance or disappearance of some components of the basin. This study focuses on the properties of a discrete dynamical system consisting of two symmetrically coupled non-invertible maps, specifically those with an invariant one-dimensional submanifold (or one-dimensional maps). These maps exhibit a complex structure of basins with the coexistence of symmetric chaotic attractors, riddled basins, blow-out, on-off intermittency, and, most significantly, the appearance of chaotic synchronization with a correlation between all the characteristics. The numerical method of critical curves can be used to demonstrate a wide range of dynamic scenarios and explain the bifurcations that lead to their occurrence. These curves play a crucial role in a system of two symmetrically coupled maps, and their significance will be discussed.

Keywords: coupled non-invertible maps; symmetry; contact bifurcations; critical curves; basins of attraction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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