1 research outputs found
Electronically--implemented coupled logistic maps
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 . 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.Comment: 8 pages, 10 figure