arXiv subjects

Miguel A. F. Sanjuán

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

At least 19 recordsLinked to original sources

arXiv2026

Nonlinear Signal Transmission and Harmonic Generation in Plasma Oscillator Chain with Coupling Asymmetry

We investigate signal transmission in a one-dimensional chain of $n$ locally coupled plasma oscillators with asymmetric bidirectional coupling $(ε_1,ε_2)$. Our results reveal a clear contrast between symmetric and asymmetric interactions: while symmetric coupling suppresses signal propagation, coupling asymmetry enables efficient nonlinear transmission across the network. In particular, sustained long range transmission is achieved when the forward coupling strength exceeds the backward coupling strength ($ε_1 > ε_2$), as demonstrated through a comprehensive phase diagram in the $(ε_1,ε_2)$ parameter space. Furthermore, under asymmetric diffusive coupling, signal transmission can persist even when the first few oscillators in the chain undergo oscillation death. A central finding of this study is the intrinsic generation of higher harmonics induced by nonlinear interactions, leading to a pronounced reversal of vibrational resonance. This nonlinear redistribution of energy facilitates selective amplification and robust propagation of specific frequency components.

nlin.CD↗

arXiv2026

Energy Transmission and Harmonic Propagation in Unidirectionally Coupled Plasma Oscillator Networks

We investigate signal transmission in a network of unidirectionally coupled plasma oscillators, where only the first oscillator is driven by a weak periodic input. As the signal propagates through the network, nonlinear interactions generate higher-order harmonic components. Spectral analysis identifies five distinct transmission patterns for the fundamental frequency and odd harmonics, and four patterns for even harmonics, encompassing damped propagation, undamped transmission, and localized amplification. The transmission characteristics are governed by both the coupling strength and system parameters. Furthermore, we analyze how variations in these key parameters shape the overall signal dynamics.

nlin.CD↗

arXiv2026

Interplay of coupling and forcing: Coherence in a nonlinear delayed oscillator

Coupled oscillators often experience two distinct influences: an internal input transmitted through coupling from a driver subsystem, and an external periodic forcing applied directly to the response. Here we ask how these two influences interact and whether their combined action can organize the response dynamics. We show that coupling and forcing can cooperate to produce a localized organization in parameter space, where the response displays simultaneously enhanced steady-state amplitudes and increased spectral concentration at the forcing frequency; we term this effect coupling-forcing induced coherence. In delay regimes where the driver approaches a steady state, the coupling acts as an effective bias that shifts the response operating point, providing a resonance-like mechanism that helps anchor the onset of the coherent band. When the driver is also externally forced, coupling-forcing induced coherence can coexist with transmitted resonance (amplification conveyed from the driver to the response through the coupling pathway). We use frequency- and time-domain diagnostics to identify parameter regions dominated by coupling-forcing induced coherence, by transmitted resonance, or by their combined action.

nlin.CD↗

arXiv2026

Bayesian Basin Tracking: Efficient Global Continuation of Multistable Dynamical Systems

Mapping the global phase space of high-dimensional multistable dynamical systems is computationally prohibitive because conventional approaches require extensive numerical integration. Here, we introduce Bayesian Basin Tracking (BBT), an adaptive Bayesian framework that exploits the persistence of basin boundaries under parameter continuation to reconstruct global phase-space structure using only a fraction of the simulations required by conventional methods. By modeling the probability that a sampled initial condition converges to a particular attractor, the method represents the phase-space geometry established at a given parameter value through a Dirichlet-multinomial model. At a nearby parameter value, these probabilities are estimated by updating the prior distribution with newly sampled data. To detect boundary crises and bifurcations autonomously, we use the log Bayes factor as an information-theoretic sensor that triggers dense resampling only when structural changes render the historical prior statistically implausible. We validate the framework using the discrete Hénon map, the continuous-time Duffing oscillator, and a 300-dimensional network of coupled Rössler oscillators. BBT overcomes the restrictive dimensional scaling of deterministic grid tessellations by concentrating the most computationally demanding calculations in structurally volatile regions. In high-dimensional synchronization landscapes, it achieves an almost sixfold computational speed-up while retaining theoretically derived error bounds.

nlin.CD↗

arXiv2026

Transmitted and Storage-Dominated Resonance in Fractionally Damped Unidirectionally Coupled Duffing Oscillators

This paper investigates resonance transmission in two unidirectionally coupled Duffing oscillators with fractional damping, where the driver is harmonically forced and the receiver is connected through a linear coupling spring. Particular attention is paid to how fractional damping in the receiver modifies amplitude amplification, energy redistribution, and the structure of the coupled response. The numerical results reveal a clear distinction between transmitted resonance, associated with a coupling-power balance consistent with direct energy transfer through the coupling spring, and storage-dominated resonance, in which the receiver still exhibits a pronounced oscillatory response while the time-averaged coupling power becomes negative under the adopted convention. In this latter regime, fractional memory promotes temporary energy accumulation within the receiver--coupling subsystem, followed by partial release through the coupling spring without any feedback on the driver dynamics. We further show that detuning the receiver natural frequency enhances the interaction between the lower-frequency transmitted response and the higher-frequency coupled response, leading to a superposed resonance regime with increased receiver amplitude, stronger localization, and sharper response. The roles of the fractional order, coupling strength, and receiver natural frequency are systematically analyzed through frequency-response curves and parametric maps. Overall, the results show how fractional memory can be used to tune resonance transmission, energy localization, and amplified response in coupled nonlinear oscillators.

nlin.CD↗

arXiv2026

High-frequency tuning of internal resonance and targeted energy transfer in a Van der Pol oscillator coupled to a nonlinear energy sink

Targeted energy transfer (TET) from a Van der Pol oscillator coupled to a nonlinear energy sink (NES) is investigated under the action of a high-frequency external drive, which tunes the effective natural stiffness and promotes resonance capture, facilitating energy transfer. Using \textit{direct partition of motion} with \textit{complexification averaging}, the mechanism of energy flow and instability control through \textit{hopf bifurcation} is characterized. A spectrally evaluated Q-factor, based on FFT at the effective slow frequency, captures the resonance peaks indicating the efficient energy transfer. Finally, the energy-dissipation metric is consistent with these Q-maps and identifies the regions where transient energy pumping is most effective.

nlin.CD↗

arXiv2026

From Basins to safe sets: a machine learning perspective on chaotic dynamics

The study of chaos has long relied on computationally intensive methods to quantify unpredictability and design control strategies. Recent advances in machine learning, from convolutional neural networks to transformer architectures, provide new ways to analyze complex phase space structures and enable real time action in chaotic dynamics. In this perspective article, we highlight how data driven approaches can accelerate classical tasks such as estimating basin characterization metrics, or partial control of transient chaos, while opening new possibilities for scalable and robust interventions in chaotic systems. In recent studies, convolutional networks have reproduced classical basin metrics with negligible bias and low computational cost, while transformer based surrogates have computed accurate safety functions within seconds, bypassing the recursive procedures required by traditional methods. We discuss current opportunities, remaining challenges, and future directions at the intersection of nonlinear dynamics and artificial intelligence.

nlin.CD↗

arXiv2026

Complex transitions between spiking, bursting and silent regimes in a new memristive Rulkov neuronal model

The Rulkov model, which simulates the behavior of biological neurons, is modified by replacing one of its control parameters with a memristive, sigmoid-type function of finite memory. This modification causes the parameter to vary according to the system's history throughout the simulation. Previous works usually modify the Rulkov model by introducing additional parameters altering its behavior. Here, by contrast, we retain the original equations and allow the control parameters to vary in time, thereby preserving the model's fundamental properties. In this sense, the proposed model is locally equivalent in time to the original one. However, unlike the original model, which reproduces a single neuronal regime per simulation, the new memristive version exhibits both uniform and chaotic transitions among multiple neuronal activity regimes. Its dynamics are examined with respect to the rate at which the memristive function changes and the number of internal states it stores. Three distinct scenarios emerge around a bifurcation point. Before the bifurcation, the system undergoes uniform transitions toward a stable bursting regime. After the bifurcation, it shows uniform transitions toward a final spiking or silent regime. At the bifurcation point, highly complex transitions arise. As examples, we present trajectories in which the neuron chaotically switches between regimes without ever settling, and trajectories for which it requires around 140000 map iterations to reach a stationary regime.

nlin.CD↗

arXiv2026

Vibrational resonance in a frequency-adaptive learning Duffing system

Vibrational resonance focuses on the resonance behavior of a nonlinear system when it is subjected to both a weak low-frequency characteristic signal and a high-frequency auxiliary signal. A traditional Duffing system has a fixed natural frequency and lacks adaptability to the excitation frequency, resulting in vibrational resonance occurring only in a lower frequency range, which affects the application of vibrational resonance. We propose a frequency-adaptive learning Duffing system to overcome the above problem through a learning rule of the natural frequency. The optimal vibrational resonance performance is demonstrated by examining the influence of auxiliary signal parameters, nonlinear stiffness coefficient and the learning rule on the response. The appearance of vibrational resonance is verified by numerical simulation, approximated theoretical predication and circuit simulation. In addition, the advantages of the proposed frequency-adaptive learning rule are highlighted in vibrational resonance performance by comparing with that of two other commonly used alternatives called Hebbian learning rules. The proposed learning rule makes the system more stable and have a stronger resonance degree. The results provide a useful reference for optimizing nonlinear system response and also for processing a weak characteristic signal through nonlinear resonance methods. These achievements provide a groundbreaking foundation for future applied studies especially in the field of weak and complex signal processing.

nlin.AO↗

arXiv2026

Vibrational resonance in coupled self-learning Duffing oscillators and its application in noisy radio frequency signal processing

This work presents a new coupled array of frequency-adaptive Duffing oscillators. Based on learning rules, the natural frequency of each oscillator changes with the external excitation to achieve the frequency-adaptive capability in the response. The frequency range of vibrational resonance in the response is greatly extended through the frequency-adaptive learning rule. Moreover, the theoretical condition for vibrational resonance is derived and its validity is verified numerically. The coupled self-learning Duffing oscillators can also perform signal denoising in strong noise environment, and its performance in signal denoising has been verified through processing the simulated signal and the wireless radio frequency signal under two scenarios. The superiority of vibrational resonance to the conventional denosing methods such as wavelet transform and Kalman filter has also been illustrated by experimental radio frequency signal processing. The combination of broadband frequency adaptability and strong noise-reduction capability suggests that these oscillators hold considerable potential for engineering applications.

nlin.AO↗

arXiv2025

Beat Frequency Induced Transitions in Synchronization Dynamics

In neurosciences, the brain processes information via the firing patterns of connected neurons operating across a spectrum of frequencies. To better understand the effects of these frequencies in the neuron dynamics, we have simulated a neuronal network of Izhikevich neurons to examine the interaction between frequency allocation and intermittent phase synchronization dynamics. As the synchronized population of neurons passes through a bifurcation, an additional frequency mode emerges, enabling a match in the mean frequency while retaining distinct most probable frequencies among neurons. Subsequently, the network intermittently transits between two patterns, one partially synchronized and the other unsynchronized. Through our analysis, we demonstrate that the frequency changes on the network lead to characteristic transition times between synchronization states. Moreover, these transitions adhere to beat frequency statistics when the neurons' frequencies differ by multiples of a frequency gap. Finally, our results can improve the performance in predicting transitions on problems where the beat frequency strongly influences the dynamics.

q-bio.NC↗

arXiv2025

AI-Driven Control of Chaos: A Transformer-Based Approach for Dynamical Systems

Chaotic behavior in dynamical systems poses a significant challenge in trajectory control, traditionally relying on computationally intensive physical models. We present a machine learning-based algorithm to compute the minimum control bounds required to confine particles within a region indefinitely, using only samples of orbits that iterate within the region before diverging. This model-free approach achieves high accuracy, with a mean squared error of $2.88 \times 10^{-4}$ and computation times in the range of seconds. The results highlight its efficiency and potential for real-time control of chaotic systems.

nlin.CD↗

arXiv2025

Stability enhanced by transient attractors in a memristive chaotic map

The introduction of a memristor in a chaotic system can significantly modify its dynamical behavior. In this paper, we couple a discrete memristor model with a chaotic map to investigate the memristor's impact on the stability of chaotic attractors. Our results reveal that introducing the memristor substantially enlarges the basin of attraction of a given chaotic attractor, thereby enhancing its stability. This phenomenon arises as a direct consequence of the memory and switching effects introduced by the memristor, which create new paths to the chaotic attractors.

nlin.CD↗

arXiv2025

Controlling Transient Chaos in the Lorenz System with Machine Learning

This paper presents a novel approach to sustain transient chaos in the Lorenz system through the estimation of safety functions using a transformer-based model. Unlike classical methods that rely on iterative computations, the proposed model directly predicts safety functions without requiring fine-tuning or extensive system knowledge. The results demonstrate that this approach effectively maintains chaotic trajectories within the desired phase space region, even in the presence of noise, making it a viable alternative to traditional methods. A detailed comparison of safety functions, safe sets, and their control performance highlights the strengths and trade-offs of the two approaches.

nlin.CD↗

arXiv2025

Characterization of Fractal Basins Using Deep Convolutional Neural Networks

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 by using deep learning techniques in which they characterize the unpredictability 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 conventional algorithm, but with a computation speed about ten times faster.

nlin.CD↗

arXiv2025

Parametric Autoresonance with Time-Delayed Control

We investigate how a constant time delay influences a parametric autoresonant system. This is a nonlinear system driven by a parametrically chirped force with a negative delay-feedback that maintains adiabatic phase locking with the driving frequency. This phase locking results in a continuous amplitude growth, regardless of parameter changes. Our study reveals a critical threshold for delay strength; above this threshold, autoresonance is sustained, while below it, autoresonance diminishes. We examine the interplay between time delay and autoresonance stability, using multi-scale perturbation methods to derive analytical results, which are corroborated by numerical simulations. Ultimately, the goal is to understand and control autoresonance stability through the time-delay parameters.

nlin.CD↗

arXiv2025

Two-Player Yorke's Game of Survival in Chaotic Transients

We present a novel two-player game in a chaotic dynamical system where players have opposing objectives regarding the system's behavior. The game is analyzed using a methodology from the field of chaos control known as partial control. Our aim is to introduce the utility of this methodology in the scope of game theory. These algorithms enable players to devise winning strategies even when they lack complete information about their opponent's actions. To illustrate the approach, we apply it to a chaotic system, the logistic map. In this scenario, one player aims to maintain the system's trajectory within a transient chaotic region, while the opposing player seeks to expel the trajectory from this region. The methodology identifies the set of initial conditions that guarantee victory for each player, referred to as the winning sets, along with the corresponding strategies required to achieve their respective objectives.

nlin.CD↗

arXiv2025

A simple method to enlarge a basin of attraction using a memristive function

This study presents an innovative approach to chaotic attractor stabilization introducing a memristor in discrete dynamical systems. Using the Hénon map as a test case, we replace a system parameter with a memristive function governed by a sigmoid activation function. The method relies on leveraging attractors with larger basins of attraction to attract the orbits and guide them towards the desired chaotic attractor. The effectiveness of the method is confirmed through numerical simulations, showing substantial enhancement in attractor stability without requiring explicit parameter control.

nlin.CD↗