Electronically-implemented coupled logistic maps

Alexandre L’Her, Pablo Amil, Nicolás Rubido, Arturo C. Marti () and Cecilia Cabeza
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Alexandre L’Her: Universidad de la República, Facultad de Ciencias, Iguá 4225
Pablo Amil: Universidad de la República, Facultad de Ciencias, Iguá 4225
Nicolás Rubido: Universidad de la República, Facultad de Ciencias, Iguá 4225
Arturo C. Marti: Universidad de la República, Facultad de Ciencias, Iguá 4225
Cecilia Cabeza: Universidad de la República, Facultad de Ciencias, Iguá 4225

The European Physical Journal B: Condensed Matter and Complex Systems, 2016, vol. 89, issue 3, 1-8

Abstract: 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.

Keywords: Statistical; and; Nonlinear; Physics (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1140/epjb/e2016-60986-8

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