X-ray spectroscopy evidence for plasma shell formation in experiments modeling accretion columns in young stars Matter and Radiation at Extremes 4, 064402 (2019);
The logistic map is a paradigmatic dynamical system originally conceived to model the discretetime 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.PACS. 0 5.45.-a -0 7.05.Fb -0 7.50.Ek
Copyright 2015 AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP PublishingMultistability in the long term dynamics of the Mackey-Glass (MG) delayed model is analyzed by using an electronic circuit capable of controlling the initial conditions. The system's phase-space is explored by varying the parameter values of two families of initial functions. The evolution equation of the electronic circuit is derived and it is shown that, in the continuous limit, it exactly corresponds to the MG model. In practice, when using a finite set of capacitors, an excellent agreement between the experimental observations and the numerical simulations is manifested. As the delay is increased, different periodic or aperiodic solutions appear. We observe abundant periodic solutions that have the same period but a different alternation of peaks of dissimilar amplitudes and propose a novel symbolic method to classify these solutions.Peer ReviewedPostprint (published version
The celebrated Mackey-Glass model describes the dynamics of physiological delayed systems in which the actual evolution depends on the values of the variables at some previous times. This kind of systems are usually expressed by delayed differential equations which turn out to be infinite-dimensional. In this contribution, an electronic implementation mimicking the Mackey-Glass model is proposed. New approaches for both the nonlinear function and the delay block are made. Explicit equations for the actual evolution of the implementation are derived. Simulations of the original equation, the circuit equation, and experimental data show great concordance.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.