arXiv subjects

Miguel A. F. Sanjuán

Publications and source records attributed to Miguel A. F. Sanjuán.

At least 37 records · Page 2Linked to original sources

arXiv2025

Vibrational resonance in the FitzHugh-Nagumo neuron model under state-dependent time delay

We propose a nonlinear one-dimensional FitzHugh--Nagumo neuronal model with an asymmetric potential driven by both a high-frequency and a low-frequency signal. Our numerical analysis focuses on the influence of a state-dependent time delay on vibrational resonance and delay-induced resonance phenomena. The response amplitude at the low-frequency is explored to characterize the vibrational resonance and delay-induced resonance. By this effort, we realize that for smaller values of the amplitude of the state-dependent time-delay velocity component, vibrational resonance and multi-resonance occur in the neuronal model. For large values of the high-frequency excitation amplitude, vibrational resonance appears with one peak. We observe a decrease in the response when the amplitude of the state-dependent time-delay velocity component increases. Also, we analyze how the state-dependent time-delay position and velocity components can give birth to delay-induced resonance for separate and together. The main results of this work are that the state-dependent time-delay velocity component can play a major role in both phenomena. In fact the parameter of the delay can control the triggering of the two resonances.

nlin.CD↗

arXiv2024

Chaotic dynamics creates and destroys branched flow

The phenomenon of branched flow, visualized as a chaotic arborescent pattern of propagating particles, waves, or rays, has been identified in disparate physical systems ranging from electrons to tsunamis, with periodic systems only recently being added to this list. Here, we explore the laws governing the evolution of the branches in periodic potentials. On one hand, we observe that branch formation follows a similar pattern in all non-integrable potentials, no matter whether the potentials are periodic or completely irregular. Chaotic dynamics ultimately drives the birth of the branches. On the other hand, our results reveal that for periodic potentials the decay of the branches exhibits new characteristics due to the presence of infinitely stable branches known as superwires. Again, the interplay between branched flow and superwires is deeply connected to Hamiltonian chaos. In this work, we explore the relationships between the laws of branched flow and the structures of phase space, providing extensive numerical and theoretical arguments to support our findings.

nlin.PS↗

arXiv2024

When a periodic forcing and a time-delayed nonlinear forcing drive a non-delayed Duffing oscillator

When two systems are coupled, the driver system can function as an external forcing over the driven or response system. Also, an external forcing can independently perturb the driven system, leading us to examine the interplay between the dynamics induced by the driver system and the external forcing acting on the response system. The cooperation of the two external perturbations can induce different kinds of behavior and initiate a resonance phenomenon. Here, we analyze and characterize this resonance phenomenon. Moreover, this resonance may coexist in the parameter set and coincide with other resonances typical of coupled systems, as {\it the transmitted resonance} and {\it the coupling-induced resonance}. Thus, we analyze the outcomes to discern their distinctions and understand when the increase in oscillation amplitudes is attributable to one phenomenon, to one of both the others, or a combination of the three.

nlin.CD↗

arXiv2024

Reverse Aperiodic Resonance in Low- to High-Dimensional Bistable Systems: A Complement to Stochastic Resonance Studies in Logic Circuits

As circuits continue to miniaturize, noise has become a significant obstacle to performance optimization. Stochastic resonance in logic circuits offers an innovative approach to harness noise constructively; however, current implementations are limited to basic logical functions such as OR, AND, NOR, and NAND, restricting broader applications. This paper introduces a three-dimensional (3D) coupling model to investigate the counterintuitive phenomena that arise in nonlinear systems under noise. Compared to the one-dimensional Langevin equation and the two-dimensional Duffing equation, the 3D coupling model features more adjustable parameters and coupling interactions, enhancing the system's dynamic behavior. The study demonstrates that increasing noise intensity triggers reverse aperiodic resonance, leading to signal phase reversal and amplitude amplification. This phenomenon is attributed to the motion of Brownian particles in a bistable potential well. Additionally, reverse aperiodic resonance addresses the lack of logical negation in traditional stochastic resonance systems by introducing noise-driven phase reversal, providing a novel alternative to conventional inverters.

nlin.AO↗

arXiv2024

Classification of Cellular Automata based on the Hamming distance

Elementary cellular automata are the simplest form of cellular automata, studied extensively by Wolfram in the 1980s. He discovered complex behavior in some of these automata and developed a classification for all cellular automata based on their phenomenology. In this paper, we present an algorithm to classify them more effectively by measuring difference patterns using the Hamming distance. Our classification aligns with Wolfram's and further categorizes them into additional subclasses.

nlin.CG↗

arXiv2024

Multiple stochastic resonances and inverse stochastic resonances in asymmetric bistable system under the ultra-high frequency excitation

Ultra-high frequency linear frequency modulation (UHF-LFM) signal, as a kind of typical non-stationary signal, has been widely used in microwave radar and other fields, with advantages such as long transmission distance, strong anti-interference ability, and wide bandwidth. Utilizing optimal dynamics response has unique advantages in weak feature identification under strong background noise. We propose a new stochastic resonance method in an asymmetric bistable system with the time-varying parameter to handle this special non-stationary signal. Interestingly, the nonlinear response exhibits multiple stochastic resonances (MSR) and inverse stochastic resonances (ISR) under UHF-LFM signal excitation, and some resonance regions may deviate or collapse due to the influence of system asymmetry. In addition, we analyze the responses of each resonance region and the mechanism and evolution law of each resonance region in detail. Finally, we significantly expand the resonance region within the parameter range by optimizing the time scale, which verifies the effectiveness of the proposed time-varying scale method. The mechanism and evolution law of MSR and ISR will provide references for researchers in related fields.

nlin.AO↗

arXiv2024

Transmitted resonance in a coupled system

When two systems are coupled, one can play the role of the driver, and the other can be the driven or response system. In this scenario, the driver system can behave as an external forcing. Thus, we study its interaction when a periodic forcing drives the driver system. In the analysis a new phenomenon shows up: when the driver system is forced by a periodic forcing, it can suffer a resonance and this resonance can be transmitted through the coupling mechanism to the driven system. Moreover, in some cases the enhanced oscillations amplitude can also interplay with a previous resonance already acting in the driven system dynamics.

nlin.AO↗

arXiv2024

Fractional damping enhances chaos in the nonlinear Helmholtz oscillator

The main purpose of this paper is to study both the underdamped and the overdamped dynamics of the nonlinear Helmholtz oscillator with a fractional order damping. For that purpose, we use the Grunwald-Letnikov fractional derivative algorithm in order to get the numerical simulations. Here, we investigate the effect of taking the fractional derivative in the dissipative term in function of the parameter a. Our main findings show that the trajectories can remain inside the well or can escape from it depending on a which plays the role of a control parameter. Besides, the parameter a is also relevant for the creation or destruction of chaotic motions. On the other hand, the study of the escape times of the particles from the well, as a result of variations of the initial conditions and the undergoing force F, is reported by the use of visualization techniques such as basins of attraction and bifurcation diagrams, showing a good agreement with previous results. Finally, the study of the escape times versus the fractional parameter a shows an exponential decay which goes to zero when a is larger than one. All the results have been carried out for weak damping where chaotic motions can take place in the non-fractional case and also for a stronger damping (overdamped case), where the influence of the fractional term plays a crucial role to enhance chaotic motions. We expect that these results can be of interest in the field of fractional calculus and its applications.

nlin.AO↗

arXiv2024

Phase control of escapes in the fractional damped Helmholtz oscillator

We analyze the nonlinear Helmholtz oscillator in the presence of fractional damping, a characteristic feature in several physical situations. In our specific scenario, as well as in the non-fractional case, for large enough excitation amplitudes, all initial conditions are escaping from the potential well. To address this, we incorporate the phase control technique into a parametric term, a feature commonly encountered in real-world situations. In the non-fractional case it has been shown that, a phase difference of {ϕ_{OPT}} \simeq π, is the optimal value to avoid the escapes of the particles from the potential well. Here, our investigation focuses on understanding when particles escape, considering both the phase difference ϕ and the fractional parameter α as control parameters. Our findings unveil the robustness of phase control, as evidenced by the consistent oscillation of the optimal ϕ value around its non-fractional counterpart when varying the fractional parameter. Additionally, our results underscore the pivotal role of the fractional parameter in governing the proportion of bounded particles, even when utilizing the optimal phase.

nlin.AO↗

arXiv2024

Systematic search for islets of stability in the standard map for large parameter values

In the seminal paper (Phys. Rep. 52, 263, 1979), Boris Chirikov showed that the standard map does not exhibit a boundary to chaos, but rather that there are small islands (islets) of stability for arbitrarily large values of the nonlinear perturbation. In this context, he established that the area of the islets in the phase space and the range of parameter values where they exist should decay following power laws with exponents -2 and -1, respectively. In this paper, we carry out a systematic numerical search for islets of stability and we show that the power laws predicted by Chirikov hold. Furthermore, we use high-resolution 3D islets to reveal that the islets volume decays following a similar power law with exponent -3.

nlin.CD↗

arXiv2024

Deep Learning-based Analysis of Basins of Attraction

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.

cs.LG↗

arXiv2024

Fractional damping induces resonant behavior in the Duffing oscillator

The interaction between the fractional order parameter and the damping parameter can play a relevant role for introducing different dynamical behaviors in a physical system. Here, we study the Duffing oscillator with a fractional damping term. Our findings show that for certain values of the fractional order parameter, the damping parameter, and the forcing amplitude high oscillations amplitude can be induced. This phenomenon is due to the appearance of a resonance in the Duffing oscillator only when the damping term is fractional.

nlin.CD↗

arXiv2024

Energy-based stochastic resetting can avoid noise-enhanced stability

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 new 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.

cond-mat.stat-mech↗

arXiv2024

Hamming distance as a measure of spatial chaos in evolutionary games

From a context of evolutionary dynamics, social games can be studied as complex systems that may converge to a Nash equilibrium. Nonetheless, they can behave in an unpredictable manner when looking at the spatial patterns formed by the agents' strategies. This is known in the literature as spatial chaos. In this paper we analyze the problem for a deterministic prisoner's dilemma and a public goods game and calculate the Hamming distance that separates two solutions that start at very similar initial conditions for both cases. The rapid growth of this distance indicates the high sensitivity to initial conditions, which is a well-known indicator of chaotic dynamics.

physics.soc-ph↗

arXiv2023

Time-delayed Duffing oscillator in an active bath

During the last decades active particles have attracted an incipient attention as they have been observed in a broad class of scenarios, ranging from bacterial suspension in living systems to artificial swimmers in nonequilibirum systems. The main feature of these particles is that they are able to gain kinetic energy from the environment, which is widely modeled by a stochastic process due to both (Gaussian) white and Ornstein-Uhlenbeck noises. In the present work, we study the nonlinear dynamics of the forced, time-delayed Duffing oscillator subject to these noises, paying special attention to their impact upon the maximum oscillations amplitude and characteristic frequency of the steady state for different values of the time delay and the driving force. Overall, our results indicate that the role of the time delay is substantially modified with respect to the situation without noise. For instance, we show that the oscillations amplitude grows with increasing noise strength when the time delay acts as a damping term in absence of noise, whereas the trajectories eventually become aperiodic when the oscillations are sustained by the time delay. In short, the interplay among the noises, forcing and time delay gives rise to a rich dynamics: a regular and periodic motion is destroyed or restored owing to the competition between the noise and the driving force depending on time delay values, whereas an erratic motion insensitive to the driving force emerges when the time delay makes the motion aperiodic. Interestingly, we also show that, for a sufficient noise strength and forcing amplitude, an approximately periodic interwell motion is promoted by means of stochastic resonance.

cond-mat.stat-mech↗

arXiv2023

Planetary Influences on the Solar Cycle: A Nonlinear Dynamics Approach

We explore the effect of some simple perturbations on three chaotic models proposed to describe large scale solar behavior via the solar dynamo theory: the Lorenz and the Rikitake systems, and a Van der Pol-Duffing oscillator. Planetary magnetic fields affecting the solar dynamo activity have been simulated by using harmonic perturbations. These perturbations introduce cycle intermittency and amplitude irregularities revealed by the frequency spectra of the nonlinear signals. Furthermore, we have found that the perturbative intensity acts as an order parameter in the correlations between the system and the external forcing. Our findings suggest a promising avenue to study the sunspot activity by using nonlinear dynamics methods.

nlin.CD↗

arXiv2023

Nonlinear delayed forcing drives a non-delayed Duffing oscillator

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.

math.DS↗

arXiv2023

Rotating cluster formations emerge in an ensemble of active particles

Rotating clusters or vortices are formations of agents that rotate around a common center. These patterns may be found in very different contexts: from swirling fish to surveillance drones. Here, we propose a minimal model for self-propelled chiral particles with inertia, which shows different types of vortices. We consider an attractive interaction for short distances on top of the repulsive interaction that accounts for volume exclusion. We study cluster formation and we find that the cluster size and clustering coefficient increase with the packing of particles. Finally, we classify three new types of vortices: encapsulated, periodic and chaotic. These clusters may coexist and their proportion depends on the density of the ensemble. The results may be interesting to understand some patterns found in nature and to design agents that automatically arrange themselves in a desired formation while exchanging only relative information.

nlin.AO↗