Further analytical bifurcation analysis and applications of coupled logistic maps

A.A. Elsadany, A.M. Yousef and Amr Elsonbaty

Applied Mathematics and Computation, 2018, vol. 338, issue C, 314-336

Abstract: In this work, we extend further the analytical study of complex dynamics exist in two coupled logistic maps. New results about the occurrence of various types of bifurcation in the system, including flip bifurcation, pitchfork bifurcation and Neimark–Sacker bifurcation are presented. To the best of authors’ knowledge, the presence of chaotic dynamics in system’s behavior has been investigated and proved analytically via Marotto’s approach for first time. Numerical simulations are carried out in order to verify theoretical results. Furthermore, chaos based encryption algorithm for images is presented as an application for the coupled logistic maps. Different scenarios of attacks are considered to demonstrate its immunity and effectiveness against the possible attacks. Finally, a circuit realization for the coupled logistic maps is proposed and utilized in a suggested real time text encryption system.

Keywords: Neimark–Sacker bifuraction; Marotto’s chaos; Image encryption; Coupled logistic map (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:338:y:2018:i:c:p:314-336

DOI: 10.1016/j.amc.2018.06.008

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