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

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Building electronic bursters with the morris–lecar neuron model
(World Scientific Publishing, 2006-01-18) Wagemakers, Alexandre; Sanjuán, Miguel A.F.; Casado, José M.; Aihara, Kazuyuki
We propose a method for the design of electronic bursting neurons, based on a simple conductance neuron model. A burster is a particular class of neuron that displays fast spiking regimes alternating with resting periods. Our method is based on the use of an electronic circuit that implements the well-known Morris–Lecar neuron model. We use this circuit as a tool of analysis to explore some regions of the parameter space and to contruct several bifurcation diagrams displaying the basic dynamical features of that system. These bifurcation diagrams provide the initial point for the design and implementation of electronic bursting neurons. By extending the phase space with the introduction of a slow driving current, our method allows to exploit the bistabilities which are present in the Morris–Lecar system to the building of different bursting models.
Characterization of Fractal Basins Using Deep Convolutional Neural Networks
(International Journal of Bifurcation and Chaos, 2022-07-12) Valle, David; Wagemakers, Alexandre; Daza, Alvar; Sanjuán, Miguel A.F.
Neural network models have recently demonstrated impressive prediction performance in complex systems where chaos and unpredictability appear. In spite of the research efforts carried out on predicting future trajectories or improving their accuracy compared to numerical methods, not sufficient work has been done on using deep learning techniques in which the unpredictability can be characterized of chaotic systems or give a general view of the global unpredictability of a system. In this work, we propose a novel approach based on deep learning techniques to measure the fractal dimension of the basins of attraction of the Duffing oscillator for a variety of parameters. As a consequence, we provide an algorithm capable of predicting fractal dimension measures as accurately as the box-counting algorithm, but with a computation speed about ten times faster.
Characterization of the local instability in the Hénon–Heiles Hamiltonian
(Elsevier, 2003-03-07) Vallejo, Juan C; Aguirre, Jacobo; Sanjuán, Miguel A.F.
Several prototypical distributions of finite-time Lyapunov exponents have been computed for the two-dimensional Hénon– Heiles Hamiltonian system. Different shapes are obtained for each dynamical state. Even when an evolution is observed in the morphology of the distributions for the smallest integration intervals, they can still serve for characterizing the dynamical state of the system.
Control of escapes in two-degree-of-freedom open Hamiltonian systems
(American Institute of Physics (AIP), 2022) Nieto, Alexandre R.; Lilienkamp, Thomas; Seoane, Jesús M.; Sanjuán, Miguel A.F.; Parlitz, Ulrich
We investigate the possibility of avoiding the escape of chaotic scattering trajectories in two-degree-of-freedom Hamiltonian systems. We develop a continuous control technique based on the introduction of coupling forces between the chaotic trajectories and some periodic orbits of the system. The main results are shown through numerical simulations, which confirm that all trajectories starting near the stable manifold of the chaotic saddle can be controlled. We also show that it is possible to jump between different unstable periodic orbits until reaching a stable periodic orbit belonging to a Kolmogorov–Arnold–Moser island.
Controlling chaos in a fluid flow past a movable cylinder
(Elsevier, 2003) Vallejo, Juan C.; Mariño, Inés P.; Sanjuán, Miguel A.F.; Kurths, Juergen
The model of a two-dimensional fluid flow past a cylinder is a relatively simple problem with a strong impact in many applied fields, such as aerodynamics or chemical sciences, although most of the involved physical mechanisms are not yet well known. This paper analyzes the fluid flow past a cylinder in a laminar regime with Reynolds number, Re, around 200, where two vortices appear behind the cylinder, by using an appropriate time-dependent stream function and applying non-linear dynamics techniques. The goal of the paper is to analyze under which circumstances the chaoticity in the wake of the cylinder might be modified, or even suppressed. And this has been achieved with the help of some indicators of the complexity of the trajectories for the cases of a rotating cylinder and an oscillating cylinder.
Deep learning-based analysis of basins of attraction
(American Institute of Physics, 2024-03-04) Valle, David; Wagemakers, Alexandre; Sanjuán, Miguel A.F.
This research addresses the challenge of characterizing the complexity and unpredictability of basins within various dynamical systems. The main focus is on demonstrating the efficiency of convolutional neural networks (CNNs) in this field. Conventional methods become computationally demanding when analyzing multiple basins of attraction across different parameters of dynamical systems. Our research presents an innovative approach that employs CNN architectures for this purpose, showcasing their superior performance in comparison to conventional methods. We conduct a comparative analysis of various CNN models, highlighting the effectiveness of our proposed characterization method while acknowledging the validity of prior approaches. The findings not only showcase the potential of CNNs but also emphasize their significance in advancing the exploration of diverse behaviors within dynamical systems.
Energy-based stochastic resetting can avoid noise-enhanced stability
(American Physical Society (APS), 2024) Cantisán, Julia; Nieto, Alexandre R.; Seoane, Jesús M.; Sanjuán, Miguel A.F.
The theory of stochastic resetting asserts that restarting a stochastic process can expedite its completion. In this paper, we study the escape process of a Brownian particle in an open Hamiltonian system that suffers noise-enhanced stability. This phenomenon implies that under specific noise amplitudes the escape process is delayed. Here, we propose a protocol for stochastic resetting that can avoid the noise-enhanced stability effect. In our approach, instead of resetting the trajectories at certain time intervals, a trajectory is reset when a predefined energy threshold is reached. The trajectories that delay the escape process are the ones that lower their energy due to the stochastic fluctuations. Our resetting approach leverages this fact and avoids long transients by resetting trajectories before they reach low-energy levels. Finally, we show that the chaotic dynamics (i.e., the sensitive dependence on initial conditions) catalyzes the effectiveness of the resetting strategy.
Ergodic decay laws in Newtonian and relativistic chaotic scattering
(Elsevier, 2021-12-01) S. Fernández, Diego; G. López, Álvaro; M. Seoane, Jesús; Sanjuán, Miguel A.F.
Experimental demonstration of bidirectional chaotic communication by means of isochronal synchronization
(IOP Publishing ; EPL Association, 2008-01-21) Wagemakers, Alexandre; Buldú, Javier M.; Sanjuán, Miguel A.F.
We give the first experimental demonstration of simultaneous bidirectional communication through chaotic carriers thanks to the phenomenon of isochronal synchronization. Two Mackey-Glass electronic circuits with chaotic behaviour exchange their signals through a coupling line with delay. When the internal feedback of the circuits and the coupling are accurately matched, isochronal synchronization arises. Under this dynamical regime, we introduce a binary message at both outputs and recover it at the opposite circuit. Finally, we discuss the security of this kind of communication system by analyzing the message recovered by a potential eavesdropper.
Final state sensitivity in noisy chaotic scattering
(Elsevier, 2021) Nieto, Alexandre R.; Seoane, Jesús M; Sanjuán, Miguel A.F.
The unpredictability in chaotic scattering problems is a fundamental topic in physics that has been studied either in purely conservative systems or in the presence of weak perturbations. In many systems noise plays an important role in the dynamical behavior and it models their internal irregularities or their coupling with the environment. In these situations the unpredictability is affected by both the chaotic dynamics and the stochastic fluctuations. In the presence of noise two trajectories with the same initial condition can evolve in different ways and converge to a different asymptotic behavior. For this reason, even the exact knowledge of the initial conditions does not necessarily lead to the predictability of the final state of the system. Hence, the noise can be considered as an important source of unpredictability that cannot be fully understood using the conventional methods of nonlinear dynamics, such as the exit basins and the uncertainty exponent. By adopting a probabilistic point of view, we develop the concepts of probability basin, uncertainty basin and noise-sensitivity exponent, that allow us to carry out both a quantitative and qualitative analysis of the unpredictability on noisy chaotic scattering problems.
Frequency dispersion in the time-delayed Kuramoto model
(American Physical Society, 2014-03-10) Nordenfelt, Anders; Wagemakers, Alexandre; Sanjuán, Miguel A.F.
We study the synchronization and frequency distribution in networks of time-delayed Kuramoto oscillators with identical natural frequency. It is found that a pronounced frequency dispersion occurs in networks with nonidentical degree distributions. The deviation of the average network frequency from its natural frequency, induced by the time delay, is identified as a necessary component for this phenomenon. Altogether this results in states intermediate between perfect synchronization and complete incoherence
Influence of the gravitational radius on asymptotic behavior of the relativistic Sitnikov problem
(American Physical Society, 2020) Bernal, Juan D.; Seoane, Jesus; Vallejo, Juan C; Huang, Liang; Sanjuán, Miguel A.F.
The Sitnikov problem is a classical problem broadly studied in physics which can represent an illustrative example of chaotic scattering. The relativistic version of this problem can be attacked by using the post- Newtonian formalism. Previous work focused on the role of the gravitational radius λ on the phase space portrait. Here we add two relevant issues on the influence of the gravitational radius in the context of chaotic scattering phenomena. First, we uncover a metamorphosis of the KAM islands for which the escape regions change insofar as λ increases. Second, there are two inflection points in the unpredictability of the final state of the system when λ ≃ 0.02 and λ ≃ 0.028. We analyze these inflection points in a quantitative manner by using the basin entropy. This work can be useful for a better understanding of the Sitnikov problem in the context of relativistic chaotic scattering. In addition, the described techniques can be applied to similar real systems, such as binary stellar systems, among others.
Isochronous synchronization in mutually coupled chaotic circuits
(American Institute of Physics, 2007-06-26) Wagemakers, Alexandre; Buldú, Javier M.; Sanjuán, Miguel A.F.
This paper examines the robustness of isochronous synchronization in simple arrays of bidirectionally coupled systems. First, the achronal synchronization of two mutually chaotic circuits, which are coupled with delay, is analyzed. Next, a third chaotic circuit acting as a relay between the previous two circuits is introduced. We observe that, despite the delay in the coupling path, the outer dynamical systems show isochronous synchronization of their outputs, i.e., display the same dynamics at exactly the same moment. Finally, we give here the first experimental evidence that the central relaying system is not required to be of the same kind of its outer counterparts.
Local predictability and nonhyperbolicity through finite Lyapunov exponent distributions in two-degrees-of-freedom Hamiltonian systems
(American Physical Society, 2008) Vallejo, Juan C; Viana, Ricardo L.; Sanjuán, Miguel A.F.
By using finite Lyapunov exponent distributions, we get insight into both the local and global properties of a dynamical flow, including its nonhyperbolic behavior. Several distributions of finite Lyapunov exponents have been computed in two prototypical four-dimensional phase-space Hamiltonian systems. They have been computed calculating the growth rates of a set of orthogonal axes arbitrarily pointed at given intervals. We analyze how such distributions serve or not for tracing the orbit nature and local flow properties such as the unstable dimension variability, as the axes are allowed or not to tend to the largest stretching direction. The relationship between the largest and closest to zero exponent distribution is analyzed. It shows a linear depen- dency at short intervals, related to the number of degrees of freedom of the system. Finally, the hyperbolicity indexes, associated to the shadowing times, are calculated. They provide interesting information at very local scales, even when there are no Gaussian distributions and the values cannot be regarded as random variables.
Measuring the transition between nonhyperbolic and hyperbolic regimes in open Hamiltonian systems
(Springer, 2020) Nieto, Alexandre R.; Zotos, Euaggelos E.; Seoane, Jesús M.; Sanjuán, Miguel A.F.
We show that the presence of KAM islands in nonhyperbolic chaotic scattering has deep implications on the unpredictability of open Hamiltonian systems. When the energy of the system increases, the particles escape faster. For this reason, the boundary of the exit basins becomes thinner and less fractal. Hence, we could expect a monotonous decrease in the unpredictability as well as in the fractal dimension. However, within the nonhyperbolic regime, fluctuations in the basin entropy have been uncovered. The reason is that when increasing the energy, both the size and geometry of the KAM islands undergo abrupt changes. These fluctuations do not appear within the hyperbolic regime. Hence, the fluctuations in the basin entropy allow us to ascertain the hyperbolic or nonhyperbolic nature of a system. In this manuscript, we have used continuous and discrete open Hamiltonian systems in order to show the relevant role of the KAM islands on the unpredictability of the exit basins, and the utility of the basin entropy to analyze this kind of systems.
Noise activates escapes in closed Hamiltonian systems
(Elsevier, 2022) Nieto, Alexandre R.; Seoane, Jesús M.; Sanjuán, Miguel A.F.
In this manuscript we show that a noise-activated escape phenomenon occurs in closed Hamiltonian systems. Due to the energy fluctuations generated by the noise, the isopotential curves open up and the particles can eventually escape in finite times. This drastic change in the dynamical behavior turns the bounded motion into a chaotic scattering problem. We analyze the escape dynamics by means of the average escape time, the probability basins and the average escape time distribution. We obtain that the main characteristics of the scattering are different from the case of noisy open Hamiltonian systems. In particular, the noise-enhanced trapping, which is ubiquitous in Hamiltonian systems, does not play the main role in the escapes. On the other hand, one of our main findings reveals a transition in the evolution of the average escape time insofar the noise is increased. This transition separates two different regimes characterized by different algebraic scaling laws. We provide strong numerical evidence to show that the complete destruction of the stickiness of the KAM islands is the key reason under the change in the scaling law. This research unlocks the possibility of modeling chaotic scattering problems by means of noisy closed Hamiltonian systems. For this reason, we expect potential application to several fields of physics such us celestial mechanics and astrophysics, among others.
Nonlinear delayed forcing drives a non-delayed Duffing oscillator
(Elsevier, 2023) Coccolo, Mattia; Sanjuán, Miguel A.F.
We study two coupled systems, one playing the role of the driver system and the other one of the driven system. The driver system is a time-delayed oscillator, and the driven or response system has a negligible delay. Since the driver system plays the role of the only external forcing of the driven system, we investigate its influence on the response system amplitude, frequency and the conditions for which it triggers a resonance in the response system output. It results that in some ranges of the coupling value, the stronger the value does not mean the stronger the synchronization, due to the arise of a resonance. Moreover, coupling means an interchange of information between the driver and the driven system. Thus, a built-in delay should be taken into account. Therefore, we study whether a delayed-nonlinear oscillator can pass along its delay to the entire coupled system and, as a consequence, to model the lag in the interchange of information between the two coupled systems.
Parametric autoresonance with time-delayed control
(American Physical Society, 2025-01-28) Somnath, Roy; Coccolo, Mattia; Sanjuán, Miguel A.F.
Investigamos cómo una demora temporal constante influye en un sistema autorresonante paramétrico. Este es un sistema no lineal impulsado por una fuerza con modulación paramétrica en frecuencia y una realimentación retardada negativa que mantiene el bloqueo de fase adiabático con la frecuencia de excitación. Este bloqueo de fase da lugar a un crecimiento continuo de la amplitud, independientemente de los cambios en los parámetros. Nuestro estudio revela un umbral crítico para la intensidad del retraso; por encima de este umbral, la autorresonancia se mantiene, mientras que por debajo de él, la autorresonancia se debilita. Examinamos la interacción entre el retraso temporal y la estabilidad de la autorresonancia, utilizando métodos de perturbación de múltiples escalas para obtener resultados analíticos, los cuales son corroborados mediante simulaciones numéricas. En última instancia, el objetivo es comprender y controlar la estabilidad de la autorresonancia a través de los parámetros de retraso temporal.
Period-doubling bifurcations and islets of stability in two-degree-of-freedom Hamiltonian systems
(American Physical Society (APS), 2023) Nieto, Alexandre R.; Seoane, Jesús M.; Sanjuán, Miguel A.F.
In this paper, we show that the destruction of the main Kolmogorov-Arnold-Moser (KAM) islands in two-degree-of-freedom Hamiltonian systems occurs through a cascade of period-doubling bifurcations. We calculate the corresponding Feigenbaum constant and the accumulation point of the period-doubling sequence. By means of a systematic grid search on exit basin diagrams, we find the existence of numerous very small KAM islands (“islets”) for values below and above the aforementioned accumulation point. We study the bifurcations involving the formation of islets and we classify them in three different types. Finally, we show that the same types of islets appear in generic two-degree-of-freedom Hamiltonian systems and in area-preserving maps.
Predicting the synchronization of a network of electronic repressilators
(World Scientific Publishing, 2010-06-01) Tokuda, Isao; Wagemakers, Alexandre; Sanjuán, Miguel A.F.
Synchronization of coupled oscillators is by now a very well studied subject. A large number of analytical and computational tools are available for the treatment of experimental results. This article focuses on a method recently proposed to construct a phase model from experimental data. The advantage of this method is that it extracts a phase model in a noninvasive manner without any prior knowledge of the experimental system. The aim of the present research is to apply this methodology to a network of electronic genetic oscillators. These electronic circuits mimic the dynamics of a synthetic genetic oscillator, called "repressilator", which is capable of synthesizing autonomous biological rhythms. The obtained phase model is shown to be capable of recovering the route leading to synchronization of genetic oscillators. The predicted onset point of synchronization agrees quite well with the experiment. This encourages further application of the present method to synthetic biological systems