Miguel A F Sanjuán

• PhD Physics
• Professor (Full) at Rey Juan Carlos University

It contains the link to the YouTube video of the speech, 'Nonlinear Dynamics, Chaos, and Complex Systems: Interdisciplinarity in the Sciences,' delivered at the Royal Academy of Sciences of Spain during the Induction Ceremony of Miguel A.F. Sanjuán on January 27, 2024. Although the speech was delivered in Spanish, it can be translated into any lang...

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 playe...

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 withi...

Transient chaos is a characteristic behaviour in nonlinear dynamics where trajectories in a certain region of phase space behave chaotically for a while, before escaping to an external attractor. In some situations, the escapes are highly undesirable, so that it would be necessary to avoid such a situation. In this paper, we apply a control method...

We propose a nonlinear FitzHugh–Nagumo neuronal model with an asymmetric potential driven by both a high-frequency signal 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 signal is ex...

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...

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 i...

This study presents an innovative approach to chaotic attractor stabilization introducing a memristor in discrete dynamical systems. Using the H\'enon 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...

When two systems are coupled, the driver system can function as an external forcing over thedriven 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 theexternal forcing acting on the response system. The cooperation of t...

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 o...

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...

Low-dose radiographic inspection is a growing trend in industry to minimize radiation risks to humans and the environment. However, reduction in radiation dose often introduces significant noise, which affects image quality and hinders accurate identification of subtle defects. This study addresses this issue by introducing a novel phenomenon calle...

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...

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...

The main properties of a dynamical system can be analyzed by examining the corresponding basins, either attraction basins in dissipative systems or escape basins in open Hamiltonian systems and area-preserving maps. In the latter case, the selection of the openings is crucial, as the way exits are chosen can directly influence the results. This stu...

Non-destructive testing of steel wire rope is significant in lifting machinery. However, it is still challenging to extract weak damage characteristics of steel wire rope under noise caused by harsh working conditions. Currently, extracting damage characteristics mostly involves secondary processing through software, which is cumbersome and ineffic...

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 di...

https://dergipark.org.tr/en/pub/chaos/issue/86422

We investigate the synchronization dynamics of a neuron network constructed using the small-world algorithm. The stochastic version of the map-based Chialvo neuron model is used to simulate each node of the network. To represent non-identical neurons, we introduce a mismatch in one of the main model parameters. Our study explores the impact of this...

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 di...

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 poten...

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...

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...

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...

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 i...

In the seminal paper, Chirikov (Phys Rep 52:263–379, 1979) 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 para...

In this paper we study different types of phase space structures which appear in the context of relativistic chaotic scattering. By using the relativistic version of the Hénon-Heiles Hamiltonian, we numerically study the topology of different kind of exit basins and compare it with the case of low velocities in which the Newtonian version of the sy...

https://dergipark.org.tr/en/pub/chaos/issue/83761

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...

Chaotic dynamical systems often exhibit transient chaos, where trajectories behave chaotically for a short amount of time before escaping to an external attractor. Sustaining transient chaotic dynamics under disturbances is challenging yet desirable for many applications. The partial control approach exploits the inherent symmetry and geometric str...

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 dif...

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 propo...

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 th...

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 d...

During recent 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 w...

We explore the effect of some simple perturbations on three nonlinear models proposed to describe large-scale solar behavior via the solar dynamo theory: the Lorenz and 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 pertu...

https://dergipark.org.tr/en/pub/chaos/issue/80150

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...

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 vi...

We study two coupled systems, one playing the role of the driver system and the other one ofthe driven system. The driver system is a time-delayed oscillator, and the driven or responsesystem has a negligible delay. Since the driver system plays the role of the only external forcingof the driven system, we investigate its influence on the response...

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...

A variation in the environment of a system, such as the temperature, the concentration of a chemical solution, or the appearance of a magnetic field, may lead to a drift in one of the parameters. If the parameter crosses a bifurcation point, the system can tip from one attractor to another (bifurcation-induced tipping). Typically, this stability ex...

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 ex...

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 interactio...

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 interactio...

We study aperiodic stochastic resonance (ASR) in a biased monostable system that subjected to different weak aperiodic pulse signals and strong noise. It is found that the biased monostable system has a unique advantage compared with the bistable system in processing the weak aperiodic pulse signals. The effects of noise, the system parameters and...

A variation in the environment of a system, such as the temperature, the concentration of a chemical solution or the appearance of a magnetic field, may lead to a drift in one of the parameters. If the parameter crosses a bifurcation point, the system can tip from one attractor to another (bifurcation-induced tipping). Typically, this stability exc...

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 simulations of the equati...

In this paper, we show that the destruction of the main 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...

https://dergipark.org.tr/en/pub/chaos/issue/75756

Animal navigation is a fascinating research field where scientists have been attempting to answer some key and basic questions explaining the mechanisms behind it. Interestingly, most of the scientific explanations for the orientation and navigation of numerous animals derive from ideas in physics. Accordingly, the main purpose of this Special Issu...

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 chao...

The basin entropy is a simple idea that aims to measure the the final state unpredictability of multistable systems. Since 2016, the basin entropy has been widely used in different contexts of physics, from cold atoms to galactic dynamics. Furthermore, it has provided a natural framework to study basins of attraction in nonlinear dynamics and new c...

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 ef...

In previous studies, double harmonic signals as external driving forces have been used for inducing logical vibrational resonance to facilitate the control of logic operations. It requires the bias parameter to break the symmetry of the bistable system. In hardware circuits, symmetric bistable system circuits are easy to build and even using few co...

Noisy scattering dynamics in the randomly driven H\'enon-Heiles system is investigated in the range of initial energies where the motion is unbounded. In this paper we study, with the help of the exit basins and the escape time distributions, how an external perturbation, be it dissipation or periodic forcing with a random phase, can enhance or mit...

https://dergipark.org.tr/en/pub/chaos/issue/73767

The basin entropy is a simple idea that aims to measure the the final state unpredictability of multistable systems. Since 2016, the basin entropy has been widely used in different contexts of physics, from cold atoms to galactic dynamics. Furthermore, it has provided a natural framework to study basins of attraction in nonlinear dynamics and new c...

We consider the nonlinear Duffing oscillator in presence of fractional damping which is characteristic in different physical situations. The system is studied with a smaller and larger damping parameter value, that we call the underdamped and overdamped regimes. In both we have studied the relation between the fractional parameter, the amplitude of...

https://dergipark.org.tr/en/pub/chaos/issue/73033

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 i...

We consider the nonlinear Duffing oscillator in presence of fractional damping which is characteristic in different physical situations. The system is studied with a smaller and larger damping parameter value, that we call the underdamped and overdamped regimes. In both we have studied the relation between the fractional parameter, the amplitude of...

The paper considers a stochastic version of the conceptual map-based Chialvo model of neural activity. Firstly, we focus on the parametric zone where this model exhibits mono- and bistability with coexistence of equilibria and oscillatory spiking attractors forming closed invariant curves. Stochastic effects of excitement and generation of bursting...

This issue is dedicated to the memory of Prof. Tenreiro Machado. https://dergipark.org.tr/en/pub/chaos/issue/64884

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 o...

In the context of nonhyperbolic chaotic scattering, it has been shown that the evolution of the KAM islands exhibits four abrupt metamorphoses that strongly affect the predictability of Hamiltonian systems. It has been suggested that these metamorphoses are related to significant changes in the structure of the KAM islands. However, previous resear...

Image denoising is a long-standing hard problem, especially in the field of engineering detection. In addition, emerging promising image-based intelligent diagnosis methods are sensitive to image noise. However, existing methods cannot meet the requirements well. Actively utilizing the construction role of noise, we propose an adaptive image denois...

A basin of attraction represents the set of initial conditions leading to a specific asymptotic state of a given dynamical system. Here, we provide a classification of the most common basins found in nonlinear dynamics with the help of the basin entropy. We have also found interesting connections between the basin entropy and other measures used to...

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 simulation...

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 o...

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 ef...

In this work, we deal with the Hénon and the Lozi map for a choice of parameters where they show transient chaos. Orbits close to the chaotic saddle behave chaotically for a while to eventually escape to an external attractor. Traditionally, to prevent such an escape, the partial control technique has been applied. This method stands out for consid...

Complex biorhythms are characteristic of ubiquitous phenomena appearing in many disciplines of human knowledge. This Special Issue collects articles devoted to different complex biorhythms phenomena such as cardiac dynamics, Covid-19 dynamics, dynamics of neural networks, cell dynamics, and a few articles devoted to general methods. It furnishes a...

Chaos Theory and Applications (March 2022 - Volume 4 - Issue 1) https://dergipark.org.tr/en/pub/chaos/issue/63571 ----------- 1) Jun MA. "Chaos Theory and Applications：The Physical Evidence, Mechanism are Important in Chaotic Systems. " 2) Burak ARICIOĞLU, Sezgin KAÇAR. "Circuit Implementation and PRNG Applications of Time Delayed Lorenz System....

Vibrational resonance (VR) shows great advantages in signal enhancement. Nonlinear frequency modulated (NLFM) signals widely exist in various fields，so it is of great significance to enhance a NLFM signal. However, for the complex NLFM signal, where its instantaneous frequency of the signal varies nonlinearly, the traditional VR method is no longer...

We reproduce the phenomenon of chemotaxis through a hybrid random walk model in two dimensions on a lattice. The dynamics of the chemoattractant is modelled using a partial differential equation, which reproduces its diffusion through the environment from its local sources. The cell is treated discretely and it is considered immersed in a medium wi...

Chaotic scattering in three dimensions has not received as much attention as in two dimensions so far. In this paper, we deal with a three-dimensional open Hamiltonian system whose Wada basin boundaries become non Wada when the critical energy value is surpassed in the absence of dissipation. In particular, we study here the dissipation effects on...

In this work we deal with the H\'enon and the Lozi map for a choice of parameters where they show transient chaos. Orbits close to the chaotic saddle behave chaotically for a while to eventually escape to an external attractor. Traditionally, to prevent such an escape, the partial control technique has been applied. This method stands out for consi...