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
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.
Key words: Statistical and Nonlinear Physics
Supplementary material in the form of three mp4 files available from the Journal web page at http://dx.doi.org/10.1140/epjb/e2016-60986-8
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2016