Electronically-implemented coupled logistic maps

A. L’Her, P. Amil, N. Rubido, A.C. Marti* (Corresponding Author), C. Cabeza

*Corresponding author for this work

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

The logistic map is a paradigmatic dynamical system originally conceived to model the discrete-time demographic growth of a population, which shockingly, shows that discrete chaos can emerge from trivial low-dimensional non-linear dynamics. In this work, we design and characterize a simple, low-cost, easy-to-handle, electronic implementation of the logistic map. In particular, our implementation allows for straightforward circuit-modifications to behave as different one-dimensional discrete-time systems. Also, we design a coupling block in order to address the behavior of two coupled maps, although, our design is unrestricted to the discrete-time system implementation and it can be generalized to handle coupling between many dynamical systems, as in a complex system. Our findings show that the isolated and coupled maps’ behavior has a remarkable agreement between the experiments and the simulations, even when fine-tuning the parameters with a resolution of ~10^{-3}. We support these conclusions by comparing the Lyapunov exponents, periodicity of the orbits, and phase portraits of the numerical and experimental data for a wide range of coupling strengths and map’s parameters.

Original languageEnglish
Article number81
JournalEuropean Physical Journal D
Volume89
DOIs
Publication statusPublished - 23 Mar 2016

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