Examinando por Autor "Seoane, Jesús M."

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A mechanism explaining the metamorphoses of KAM islands in nonhyperbolic chaotic scattering
(Springer, 2022) Nieto, Alexandre R.; Seoane, Jesús M.; Barrio, Roberto; Sanjuán, Miguel A. F.
Abstract 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 research has not provided an explanation of the mechanisms underlying the metamorphoses. Here, we show that they occur due to the formation of a homoclinic or heteroclinic tangle that breaks the internal structure of the main KAM island. We obtain similar qualitative results in a two-dimensional Hamiltonian system and a twodimensional area-preserving map. The equivalence of the results obtained in both systems suggests that the same four metamorphoses play an important role in conservative systems.
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.
Delay-Induced Resonance in the Time-Delayed Duffing Oscillator
(World Scientific Publishing, 2020) Cantisan, Julia; Coccolo, Mattia; Seoane, Jesús M.; F. Sanjuan, Miguel A.
The phenomenon of delay-induced resonance implies that in a nonlinear system a time-delay term may be used as an effective enhancer of the oscillations caused by an external forcing maintaining the same frequency. This is possible for the parameters for which the time-delay induces sustained oscillations. Here, we study this type of resonance in the overdamped and underdamped time-delayed Duffing oscillators, and we explore some new features. One of them is the conjugate phenomenon: the oscillations caused by the time-delay may be enhanced by means of the forcing without modifying their frequency. The resonance takes place when the frequency of the oscillations induced by the time-delay matches the ones caused by the forcing and vice versa. This is an interesting result as the nature of both perturbations is different. Even for the parameters for which the time-delay does not induce sustained oscillations, we show that a resonance may appear following a different mechanism.
Delay-induced resonance suppresses damping-induced unpredictability
(The Royal Society, 2020) Cantisan, Julia; Coccolo, Mattia; Seoane, Jesús M.; F. Sanjuan, Miguel A.; Rajasekar, S.
Combined effects of the damping and forcing in the underdamped time-delayed Duffing oscillator are considered in this paper. We analyse the generation of a certain damping-induced unpredictability due to the gradual suppression of interwell oscillations. We find the minimal amount of the forcing amplitude and the right forcing frequency to revert the effect of the dissipation, so that the interwell oscillations can be restored, for different time delay values. This is achieved by using the delay-induced resonance, in which the time delay replaces one of the two periodic forcings present in the vibrational resonance. A discussion in terms of the time delay of the critical values of the forcing for which the delay-induced resonance can tame the dissipation effect is finally carried out.
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.
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.
Noise-induced complex dynamics and synchronization in the map-based Chialvo neuron model
(Elsevier, 2023-01) Bashkirtseva, Irina; Ryashko, Lev; Used, Javier; Seoane, Jesús M.; Fernández Sanjuán, Miguel Ángel
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 monoand bistability with coexistence of equilibria and oscillatory spiking attractors forming closed invariant curves. Stochastic effects of excitement and generation of bursting are studied both numerically and analytically by confidence ellipses. A phenomenon of the noise-induced transition to chaos in a localized two-parametric zone is discussed. Besides, we also study the phenomenon of synchronization between neurons by using a two-neuron network with a small coupling. In this scenario, we have found critical values of noise for which we obtain a good performance for the synchronization between the neurons of the network.
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.
Rate and memory effects in bifurcation-induced tipping
(American Physical Society (APS), 2023) Cantisán, Julia; Yanchuk, Serhiy; Seoane, Jesús M.; F. Sanjuan, Miguel A.
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 exchange occurs at a parameter value beyond the bifurcation value. This is what we call, here, the shifted stability exchange. We perform a systematic study on how the shift is affected by the initial parameter value and its change rate. To that end, we present numerical simulations and partly analytical results for different types of bifurcations and different paradigmatic systems. We show that the nonautonomous dynamics can be split into two regimes. Depending on whether we exceed the numerical or experimental precision or not, the system may enter the nondeterministic or the deterministic regime. This is determined solely by the conditions of the drift. Finally, we deduce the scaling laws governing this phenomenon and we observe very similar behavior for different systems and different bifurcations in both regimes.
Resonant behavior and unpredictability in forced chaotic scattering
(American Physical Society (APS), 2018) Nieto, Alexandre R.; Seoane, Jesús M.; Alvarellos, J. E.; Sanjuán, Miguel A.F.
Chaotic scattering in open Hamiltonian systems is a topic of fundamental interest in physics, which has been mainly studied in the purely conservative case. However, the effect of weak perturbations in this kind of system has been an important focus of interest in the past decade. In a previous work, the authors studied the effects of a periodic forcing in the decay law of the survival probability, and they characterized the global properties of escape dynamics. In the present paper, we add two important issues in the effects of periodic forcing: the fractal dimension of the set of singularities in the scattering function and the unpredictability of the exit basins, which is estimated by using the concept of basin entropy. Both the fractal dimension and the basin entropy exhibit a resonant-like decrease as the forcing frequency increases. We provide a theoretical reasoning which could justify this decreasing in the fractality near the main resonant frequency that appears for ω ≈ 1. We attribute the decrease in the basin entropy to the reduction of the area occupied by the Kolmogorov-Arnold-Moser (KAM) islands and the basin boundaries when the frequency is close to the resonance. On the other hand, the decay rate of the exponential decay law shows a minimum value of the amplitude, Ac, which reflects the complete destruction of the KAM islands in the resonance. Finally, we have found the existence of Wada basins for a wide range of values of the frequency and the forcing amplitude. We expect that this work could be potentially useful in research fields related to chaotic Hamiltonian pumps and oscillations in chemical reactions and companion galaxies, among others.
Rotating cluster formations emerge in an ensemble of active particles
(Elsevier, 2023) Cantisan, Julia; Seoane, Jesús M.; F. Sanjuan, Miguel A.
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.
Stochastic resetting in the Kramers problem: A Monte Carlo approach
(Elsevier, 2021) Cantisan, Julia; Seoane, Jesús M.; F. Sanjuan, Miguel A.
The theory of stochastic resetting asserts that restarting a search process at certain times may accelerate the finding of a target. In the case of a classical diffusing particle trapped in a potential well, stochastic resetting may decrease the escape times due to thermal fluctuations. Here, we numerically explore the Kramers problem for a cubic potential, which is the simplest potential with a escape. Both deterministic and Poisson resetting times are analyzed. We use a Monte Carlo approach, which is necessary for generic complex potentials, and we show that the optimal rate is related to the escape times distribution in the case without resetting. Furthermore, we find rates for which resetting is beneficial even if the resetting position is located on the contrary side of the escape.
The role of noise in the tumor dynamics under chemotherapy treatment
(Springer, 2021) Bashkirtseva, Irina; Ryashko, Lev; Duarte, Jorge; Seoane, Jesús M.; Sanjuán, Miguel A. F.
Dynamical systems modeling tumor growth have been investigated to analyze the dynamics between tumor and healthy cells. Recent theoretical studies indicate that these interactions may lead to different dynamical outcomes under the effect of particular cancer therapies. In the present paper, we derive a system of nonlinear differential equations, in order to investigate solid tumors in vivo, taking into account the impact of chemotherapy on both tumor and healthy cells. We start by studying our model only in terms of deterministic dynamics under the variation of a drug concentration parameter. Later, with the introduction of noise, a stochastic model is used to analyze the impact of the unavoidable random fluctuations. As a result, new insights into noise-induced transitions are provided and illustrated in detail using techniques from dynamical systems and from the theory of stochastic processes.
Transient chaos in time-delayed systems subjected to parameter drift
(IOP Publishing, 2021) Cantisan, Julia; Seoane, Jesús M.; F. Sanjuan, Miguel A.
External and internal factors may cause a system's parameter to vary with time before it stabilizes. This drift induces a regime shift when the parameter crosses a bifurcation. Here, we study the case of an infinite dimensional system: a time-delayed oscillator whose time delay varies at a small but non-negligible rate. Our research shows that due to this parameter drift, trajectories from a chaotic attractor tip to other states with a certain probability. This causes the appearance of the phenomenon of transient chaos. By using an ensemble approach, we find a gamma distribution of transient lifetimes, unlike in other non-delayed systems where normal distributions have been found to govern the process. Furthermore, we analyze how the parameter change rate influences the tipping probability, and we derive a scaling law relating the parameter value for which the tipping takes place and the lifetime of the transient chaos with the parameter change rate.
Transient dynamics of the Lorenz system with a parameter drift
(World Scientific Publishing, 2021) Cantisan, Julia; F. Sanjuan, Miguel A.; Seoane, Jesús M.
Nonautonomous dynamical systems help us to understand the implications of real systems which are in contact with their environment as it actually occurs in nature. Here, we focus on systems where a parameter changes with time at small but non-negligible rates before settling at a stable value, by using the Lorenz system for illustration. This kind of systems commonly show a long-term transient dynamics previous to a sudden transition to a steady state. This can be explained by the crossing of a bifurcation in the associated frozen-in system. We surprisingly uncover a scaling law relating the duration of the transient to the rate of change of the parameter for a case where a chaotic attractor is involved. Additionally, we analyze the viability of recovering the transient dynamics by reversing the parameter to its original value, as an alternative to the control theory for systems with parameter drifts. We obtain the relationship between the paramater change rate and the number of trajectories that tip back to the initial attractor corresponding to the transient state.
Trapping enhanced by noise in nonhyperbolic and hyperbolic chaotic scattering
(Elsevier, 2021) Nieto, Alexandre R.; Seoane, Jesús M.; Sanjuán, Miguel A. F.
The noise-enhanced trapping is a surprising phenomenon that has already been studied in chaotic scattering problems where the noise affects the physical variables but not the parameters of the system. Following this research, in this work we provide strong numerical evidence to show that an additional mechanism that enhances the trapping arises when the noise influences the energy of the system. For this purpose, we have included a source of Gaussian white noise in the HȨnon-Heiles system, which is a paradigmatic example of open Hamiltonian system. For a particular value of the noise intensity, some trajectories decrease their energy due to the stochastic fluctuations. This drop in energy allows the particles to spend very long transients in the scattering region, increasing their average escape times. This result, together with the previously studied mechanisms, points out the generality of the noise-enhanced trapping in chaotic scattering problems.