Examinando por Autor "F. Sanjuán, Miguel A."

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Controlling the bursting size in the two-dimensional Rulkov model
(Elsevier, 2023) López, Jennifer; Coccolo, Mattia; Capeáns, Rubén; F. Sanjuán, Miguel A.
We propose to control the orbits of the two-dimensional Rulkov model affected by bounded noise. For the correct parameter choice the phase space presents two chaotic regions separated by a transient chaotic region in between. One of the chaotic regions is the responsible to give birth to the neuronal bursting regime. Normally, an orbit in this chaotic region cannot pass through the transient chaotic one and reach the other chaotic region. As a consequence the burstings are short in time. Here, we propose a control technique to connect both chaotic regions and allow the neuron to exhibit very long burstings. This control method defines a region Q covering the transient chaotic region where it is possible to find an advantageous set S ⊂ Q through which the orbits can be driven with a minimal control. In addition we show how the set S changes depending on the noise intensity affecting the map, and how the set S can be used in different scenarios of control.
Using the basin entropy to explore bifurcations
(Elsevier, 2023) Wagemakers, Alexandre; Daza, Alvar; F. Sanjuán, Miguel A.
Bifurcation theory is the usual analytic approach to study the parameter space of a dynamical system. Despite the great power of prediction of these techniques, fundamental limitations appear during the study of a given problem. Nonlinear dynamical systems often hide their secrets and the ultimate resource is the numerical simulation of the equations. This paper presents a method to explore bifurcations by using the basin entropy. This measure of the unpredictability can detect transformations of phase space structures as a parameter evolves. We present several examples where the bifurcations in the parameter space have a quantitative effect on the basin entropy. Moreover, some transformations, such as the basin boundary metamorphoses, can be identified with the basin entropy but are not reflected in the bifurcation diagram. The correct interpretation of the basin entropy plotted as a parameter extends the numerical exploration of dynamical systems.