The dynamics of coupled logistic maps

J.S. Cánovas; J.S. Cánovas

doi:10.3934/nhm.2023010

Networks and Heterogeneous Media

2023, Volume 18, Issue 1: 275-290. doi: 10.3934/nhm.2023010

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The dynamics of coupled logistic maps

J.S. Cánovas ^,

Department of Applied Mathematics and Statistics, Technical University of Cartagena, Cartagena, 30202, Spain

Received: 03 October 2022 Revised: 24 November 2022 Accepted: 01 December 2022 Published: 20 December 2022

This paper considers a coupled system given by two logistic maps with the same parameter. We studied the existence and stability of fixed points outside the diagonal and estimated the regions where the synchronization to the diagonal, both chaotic and regular, is possible. Bifurcation scenarios to illustrate the results are also given.
- coupled systems,
- logistic map,
- synchronization,
- Lyapunov exponents,
- bifurcations
Citation: J.S. Cánovas. The dynamics of coupled logistic maps[J]. Networks and Heterogeneous Media, 2023, 18(1): 275-290. doi: 10.3934/nhm.2023010

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Abstract

This paper considers a coupled system given by two logistic maps with the same parameter. We studied the existence and stability of fixed points outside the diagonal and estimated the regions where the synchronization to the diagonal, both chaotic and regular, is possible. Bifurcation scenarios to illustrate the results are also given.

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