arXiv subjects

Miguel A. F. Sanjuan

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

15 recordsLinked to original sources

arXiv2025

Stochastic birhythmicity outside the coexistence region in the Hindmarsh-Rose model

In this work, we demonstrate that the Hindmarsh-Rose model subjected to additive white noise exhibits birhythmicity. Specifically, the system fluctuates between two distinct bursting attractors characterized by different numbers of spikes. This behavior is observed not only within the bistable region bounded by two saddle-node bifurcations of limit cycles but also beyond these boundaries. This phenomenon is associated with the ghost effect, typically observed near deterministic saddle-node bifurcations. We map the region of stochastic birhythmicity in terms of the noise intensity and a key deterministic parameter that controls the dynamics of fast ion channels. To provide an analytical foundation, we introduce a simple stochastic model with a single saddle-node bifurcation. In this model, stochastic birhythmicity is similarly characterized as a function of noise intensity and the control parameter.

nlin.AO↗

arXiv2024

Synchronization of two non-identical Chialvo neurons

We investigate the synchronization between two neurons using the stochastic version of the map-based Chialvo model. To simulate non-identical neurons, a mismatch is introduced in one of the main parameters of the model. Subsequently, the synchronization of the neurons is studied as a function of this mismatch, the noise introduced in the stochastic model, and the coupling strength between the neurons. We propose the simplest neuron network for study, as its analysis is more straightforward and does not compromise generality. Within this network, two nonidentical neuron maps are electrically coupled. In order to understand if specific behaviors affect the global behavior of the system, we consider different cases related to the behavior of the neurons (chaotic or periodic). Furthermore, we study how variations in model parameters affect the firing frequency in all cases. Additionally, we consider that the two neurons have both excitatory and inhibitory couplings. Consequently, we identify critical values of noise and mismatch for achieving satisfactory synchronization between the neurons in both cases. Finally, we conjecture that the results are of a general nature and are applicable to different neuron models.

nlin.CD↗

arXiv2024

Vibrational resonance: A review

Over the past two decades, vibrational resonance has garnered significant interest and evolved into a prominent research field. Classical vibrational resonance examines the response of a nonlinear system excited by two signals: a weak, slowly varying characteristic signal, and a fast-varying auxiliary signal. The characteristic signal operates on a much longer time scale than the auxiliary signal. Through the cooperation of the nonlinear system and these two excitations, the faint input can be substantially amplified, showcasing the constructive role of the fast-varying signal. Since its inception, vibrational resonance has been extensively studied across various disciplines, including physics, mathematics, biology, neuroscience, laser science, chemistry, and engineering. Here, we delve into a detailed discussion of vibrational resonance and the most recent advances, beginning with an introduction to characteristic signals commonly used in its study. Furthermore, we compile numerous nonlinear models where vibrational resonance has been observed to enhance readers' understanding and provide a basis for comparison. Subsequently, we present the metrics used to quantify vibrational resonance, as well as offer a theoretical formulation. This encompasses the method of direct separation of motions, linear and nonlinear vibrational resonance, re-scaled vibrational resonance, ultrasensitive vibrational resonance, and the role of noise in vibrational resonance. Later, we showcase two practical applications of vibrational resonance: one in image processing and the other in fault diagnosis. This presentation offers a comprehensive and versatile overview of vibrational resonance, exploring various facets and highlighting promising avenues for future research in both theory and engineering applications.

nlin.AO↗

arXiv2023

Ultrasensitive vibrational resonance induced by small disturbances

We have found two kinds of ultra-sensitive vibrational resonance in coupled nonlinear systems. It is particularly worth pointing out that this ultra-sensitive vibrational resonance is a transient behavior caused by transient chaos. Considering long-term response, the system will transform from transient chaos to periodic response. The pattern of vibrational resonance will also transform from ultra-sensitive vibrational resonance to conventional vibrational resonance. This article focuses on the transient ultra-sensitive vibrational resonance phenomenon. It is induced by a small disturbance of the high-frequency excitation and the initial simulation conditions, respectively. The damping coefficient and the coupling strength are the key factors to induce the ultra-sensitive vibrational resonance. By increasing these two parameters, the vibrational resonance pattern can be transformed from an ultra-sensitive vibrational resonance to a conventional vibrational resonance. The reason for different vibrational resonance patterns to occur lies in the state of the system response. The response usually presents transient chaotic behavior when the ultra-sensitive vibrational resonance appears and the plot of the response amplitude versus the controlled parameters shows a highly fractalized pattern. When the response is periodic or doubly-periodic, it usually corresponds to the conventional vibrational resonance. The ultra-sensitive vibrational resonance not only occurs at the excitation frequency, but it also occurs at some more nonlinear frequency components. The ultra-sensitive vibrational resonance as a transient behavior and the transformation of vibrational resonance patterns are new phenomena in coupled nonlinear systems.

nlin.PS↗

arXiv2023

Harmonic-Gaussian double-well potential stochastic resonance with its application to enhance weak fault characteristics of machinery

Noise is ubiquitous and unwanted in detecting weak signals, which would give rise to incorrect filtering frequency-band selection in signal filtering-based methods including fast kurtogram, teager energy operators and wavelet packet transform filters and meanwhile would result in incorrect selection of useful components and even mode mixing, end effects and etc. in signal decomposition-based methods including empirical mode decomposition, singular value decomposition and local mean decomposition. On the contrary, noise in stochastic resonance (SR) is beneficial to enhance weak signals of interest embedded in signals with strong background noise. Taking into account that nonlinear systems are crucial ingredients to activate the SR, here we investigate the SR in the cases of overdamped and underdamped harmonic-Gaussian double-well potential systems subjected to noise and a periodic signal. We derive and measure the analytic expression of the output signal-to-noise ratio (SNR) and the steady-state probability density (SPD) function under approximate adiabatic conditions. When the harmonic-Gaussian double-well potential loses its stability, we can observe the antiresonance phenomenon, whereas adding the damped factor into the overdamped system can change the stability of the harmonic-Gaussian double-well potential, resulting that the antiresonance behavior disappears in the underdamped system. Then, we use the overdamped and underdamped harmonic-Gaussian double-well potential SR to enhance weak useful characteristics for diagnosing incipient rotating machinery failures.

physics.app-ph↗

arXiv2022

Time-dependent effects hinder cooperation on the public goods game

The public goods game is a model of a society investing some assets and regaining a profit, although can also model biological populations. In the classic public goods game only two strategies compete: either cooperate or defect; a third strategy is often implemented to asses punishment, which is a mechanism to promote cooperation. The conditions of the game can be of a dynamical nature, therefore we study time-dependent effects such an as oscillation in the enhancement factor, which accounts for productivity changes over time. Furthermore, we continue to study time dependencies on the game with a delay on the punishment time. We conclude that both the oscillations on the productivity and the punishment delay concur in the detriment of cooperation.

nlin.AO↗

arXiv2021

Noise activates escapes in closed Hamiltonian systems

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.

nlin.CD↗

arXiv2020

Unpredictability, Uncertainty and Fractal Structures in Physics

In Physics, we have laws that determine the time evolution of a given physical system, depending on its parameters and its initial conditions. When we have multi-stable systems, many attractors coexist so that their basins of attraction might possess fractal or even Wada boundaries in such a way that the prediction becomes more complicated depending on the initial conditions. Chaotic systems typically present fractal basins in phase space. A small uncertainty in the initial conditions gives rise to a certain unpredictability of the final state behavior. The new notion of basin entropy provides a new quantitative way to measure the unpredictability of the final states in basins of attraction. Simple methods from chaos theory can contribute to a better understanding of fundamental questions in physics as well as other scientific disciplines.

nlin.CD↗

arXiv2020

How to detect Wada Basins

We present a review of the different techniques available to study a special kind of fractal basins of attraction known as Wada basins, which have the intriguing property of having a single boundary separating three or more basins. We expose several approaches to identify this topological property that rely on different, but not exclusive, definitions of the Wada property.

nlin.CD↗

arXiv2020

Artificial Intelligence, Chaos, Prediction and Understanding in Science

Machine learning and deep learning techniques are contributing much to the advancement of science. Their powerful predictive capabilities appear in numerous disciplines, including chaotic dynamics, but they miss understanding. The main thesis here is that prediction and understanding are two very different and important ideas that should guide us about the progress of science. Furthermore, it is emphasized the important role played by that nonlinear dynamical systems for the process of understanding. The path of the future of science will be marked by a constructive dialogue between big data and big theory, without which we cannot understand.

cs.GL↗

arXiv2018

Low-dimensional paradigms for high-dimensional hetero-chaos

The dynamics on a chaotic attractor can be quite heterogeneous, being much more unstable in some regions than others. Some regions of a chaotic attractor can be expanding in more dimensions than other regions. Imagine a situation where two such regions and each contains trajectories that stay in the region for all time while typical trajectories wander throughout the attractor. Such an attractor is "hetero-chaotic" (i.e. it has heterogeneous chaos) if furthermore arbitrarily close to each point of the attractor there are points on periodic orbits that have different unstable dimensions. This is hard to picture but we believe that most physical systems possessing a high-dimensional attractor are of this type. We have created simplified models with that behavior to give insight to real high-dimensional phenomena.

nlin.CD↗

arXiv2018

The continuous route to multi-chaos

For low-dimensional chaotic attractors there is usually a single number of unstable dimensions for all of its periodic orbits and we can say such attractors exhibit "mono-chaos". In high-dimensional chaotic attractors, trajectories are prone to travel through quite different regions of phase space, some far more unstable than others. This heterogeneity makes predictability even more difficult than in low-dimensional homogeneous chaotic attractors. A chaotic attractor is "multi-chaotic" if every point of the attractor is arbitrarily close to periodic points with different numbers of unstable dimensions. We believe that most physical systems possessing a high-dimensional attractor are of this type. We make three conjectures about multi-chaos which we explore using three two-dimensional paradigmatic examples of multi-chaotic attractors. They can be thought of as small-scale examples that give insight for real high-dimensional phenomena. We find a single route from mono-chaos to multi-chaos if an attractor changes continuously as a parameter is varied. This multi-chaos bifurcation (MCB) is a periodic orbit bifurcation; one branch of periodic orbits is created with a number of unstable dimensions that is different from the mono-chaos.

nlin.CD↗

arXiv2017

The dose-dense principle in chemotherapy

Chemotherapy is a class of cancer treatment that uses drugs to kill cancer cells. A typical chemotherapeutic protocol consists of several drugs delivered in cycles of three weeks. We present mathematical analyses demonstrating the existence of a maximum time between cycles of chemotherapy for a protocol to be effective. A mathematical equation is derived, which relates such a maximum time with the variables that govern the kinetics of the tumor and those characterizing the chemotherapeutic treatment. Our results suggest that there are compelling arguments supporting the use of dose-dense protocols. Finally, we discuss the limitations of these protocols and suggest an alternative.

q-bio.PE↗

arXiv2017

Supply based on demand dynamical model

We propose and analyze numerically a simple dynamical model that describes the firm behaviors under uncertainty of demand forecast. Iterating this simple model and varying some parameters values we observe a wide variety of market dynamics such as equilibria, periodic and chaotic behaviors. Interestingly the model is also able to reproduce market collapses.

q-fin.GN↗

arXiv2013

Vibrational resonance in groundwater-dependent plant ecosystems

We report the phenomenon of vibrational resonance in a single species and a two species models of groundwater-dependent plant ecosystems with a biharmonic oscillation (with two widely different frequencies ωand Ω, Ω>> ω) of the water table depth. In these two systems, the response amplitude of the species biomass shows multiple resonances with different mechanisms. The resonance occurs at both low- and high-frequencies of the biharmonic force. In the single species bistable system, the resonance occurs at discrete values of the amplitude g of the high-frequency component of the water table. Furthermore, the best synchronization of biomass and its carrying capacity with the biharmonic force occurs at the resonance. In the two species excitable and time-delay model, the response amplitude (Q) profile shows several plateau regions of resonance, where the period of evolution of the species biomass remains the same and the value of Q is inversely proportional to it. The response amplitude is highly sensitive to the time-delay parameter τand shows two distinct sequences of resonance intervals with a decreasing amplitude with τ.

nlin.CD↗