Eur. Phys. J. B (2016) 89: 81
https://doi.org/10.1140/epjb/e2016-60986-8

Regular Article

Electronically-implemented coupled logistic maps^*

¹ Universidad de la República, Facultad de Ciencias, Iguá 4225, Montevideo, Uruguay
² University of Aberdeen, King’s College, Institute for Complex Systems and Mathematical Biology, Aberdeen, AB24 3UE, UK

^a e-mail: marti@fisica.edu.uy

Received: 30 December 2015
Received in final form: 4 February 2016
Published online: 23 March 2016

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.