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  1. Article ; Online: Hamming distance as a measure of spatial chaos in evolutionary games.

    Alfaro, Gaspar / Sanjuán, Miguel A F

    Physical review. E

    2024  Volume 109, Issue 1-1, Page(s) 14203

    Abstract: 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. ...

    Abstract 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.
    Language English
    Publishing date 2024-02-15
    Publishing country United States
    Document type Journal Article
    ZDB-ID 2844562-4
    ISSN 2470-0053 ; 2470-0045
    ISSN (online) 2470-0053
    ISSN 2470-0045
    DOI 10.1103/PhysRevE.109.014203
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  2. Article ; Online: Deep learning-based analysis of basins of attraction.

    Valle, David / Wagemakers, Alexandre / Sanjuán, Miguel A F

    Chaos (Woodbury, N.Y.)

    2024  Volume 34, Issue 3

    Abstract: 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 ... ...

    Abstract 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.
    Language English
    Publishing date 2024-03-04
    Publishing country United States
    Document type Journal Article
    ZDB-ID 1472677-4
    ISSN 1089-7682 ; 1054-1500
    ISSN (online) 1089-7682
    ISSN 1054-1500
    DOI 10.1063/5.0159656
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  3. Article ; Online: Energy-based stochastic resetting can avoid noise-enhanced stability.

    Cantisán, Julia / Nieto, Alexandre R / Seoane, Jesús M / Sanjuán, Miguel A F

    Physical review. E

    2024  Volume 109, Issue 2-1, Page(s) 24201

    Abstract: 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 ... ...

    Abstract 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.
    Language English
    Publishing date 2024-03-15
    Publishing country United States
    Document type Journal Article
    ZDB-ID 2844562-4
    ISSN 2470-0053 ; 2470-0045
    ISSN (online) 2470-0053
    ISSN 2470-0045
    DOI 10.1103/PhysRevE.109.024201
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  4. Article ; Online: Period-doubling bifurcations and islets of stability in two-degree-of-freedom Hamiltonian systems.

    Nieto, Alexandre R / Seoane, Jesús M / Sanjuán, Miguel A F

    Physical review. E

    2023  Volume 107, Issue 5-1, Page(s) 54215

    Abstract: 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 ... ...

    Abstract 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.
    MeSH term(s) Computer Simulation ; Nonlinear Dynamics
    Language English
    Publishing date 2023-06-16
    Publishing country United States
    Document type Journal Article
    ZDB-ID 2844562-4
    ISSN 2470-0053 ; 2470-0045
    ISSN (online) 2470-0053
    ISSN 2470-0045
    DOI 10.1103/PhysRevE.107.054215
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  5. Article ; Online: Planetary influences on the solar cycle: A nonlinear dynamics approach.

    Muñoz, Juan M / Wagemakers, Alexandre / Sanjuán, Miguel A F

    Chaos (Woodbury, N.Y.)

    2023  Volume 33, Issue 12

    Abstract: 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 ... ...

    Abstract 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 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.
    Language English
    Publishing date 2023-12-04
    Publishing country United States
    Document type Journal Article
    ZDB-ID 1472677-4
    ISSN 1089-7682 ; 1054-1500
    ISSN (online) 1089-7682
    ISSN 1054-1500
    DOI 10.1063/5.0166920
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  6. Article ; Online: Introduction to Focus Issue: Recent advances in modeling complex systems: Theory and applications.

    Awrejcewicz, Jan / Sanjuán, Miguel A F

    Chaos (Woodbury, N.Y.)

    2021  Volume 31, Issue 7, Page(s) 70401

    Abstract: This is an introductory paper of the Focus Issue Recent advances in modeling complex systems: Theory and applications, where papers presenting new advances and insights into chaotic dynamics, fractional dynamics, complex oscillations, complex traffic ... ...

    Abstract This is an introductory paper of the Focus Issue Recent advances in modeling complex systems: Theory and applications, where papers presenting new advances and insights into chaotic dynamics, fractional dynamics, complex oscillations, complex traffic dynamics, and complex networks, as well as their applications, are collected. All these different problems share common ideas and methods and provide new perspectives for further progress in the modeling of complex systems.
    Language English
    Publishing date 2021-08-03
    Publishing country United States
    Document type Editorial
    ZDB-ID 1472677-4
    ISSN 1089-7682 ; 1054-1500
    ISSN (online) 1089-7682
    ISSN 1054-1500
    DOI 10.1063/5.0061767
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  7. Book ; Online: Artificial Intelligence, Chaos, Prediction and Understanding in Science

    Sanjuan, Miguel A. F.

    2020  

    Abstract: 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 ... ...

    Abstract 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.
    Keywords Computer Science - General Literature
    Publishing date 2020-03-03
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  8. Book ; Online: Deep Learning-based Analysis of Basins of Attraction

    Valle, David / Wagemakers, Alexandre / Sanjuán, Miguel A. F.

    2023  

    Abstract: This study showcases the effectiveness of convolutional neural networks (CNNs) in characterizing the complexity and unpredictability of basins of attraction for diverse dynamical systems. This novel method is optimal for exploring different parameters of ...

    Abstract This study showcases the effectiveness of convolutional neural networks (CNNs) in characterizing the complexity and unpredictability of basins of attraction for diverse dynamical systems. This novel method is optimal for exploring different parameters of dynamical systems since the conventional methods are computationally expensive for characterizing multiple basins of attraction. Additionally, our research includes a comparison of different CNN architectures for this task showing the superiority of our proposed characterization method over the conventional methods, even with obsolete architectures.
    Keywords Computer Science - Machine Learning
    Publishing date 2023-09-27
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  9. Book ; Online: Time-delayed Duffing oscillator in an active bath

    Valido, Antonio A. / Coccolo, Mattia / Sanjuán, Miguel A. F.

    2023  

    Abstract: 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 ... ...

    Abstract 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.

    Comment: 12+1 pages, 10 figures. Comments are welcome. Substantial changes with respect to the first version: an introduction of previous works is included, stochastic resonance effects are now treated, discussion has been partiatly modified, the vast majority of figures were replaced
    Keywords Condensed Matter - Statistical Mechanics ; Nonlinear Sciences - Chaotic Dynamics ; Physics - Biological Physics
    Subject code 612
    Publishing date 2023-08-22
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  10. Article ; Online: Rate and memory effects in bifurcation-induced tipping.

    Cantisán, Julia / Yanchuk, Serhiy / Seoane, Jesús M / Sanjuán, Miguel A F / Kurths, Jürgen

    Physical review. E

    2023  Volume 108, Issue 2-1, Page(s) 24203

    Abstract: 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 ... ...

    Abstract 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.
    Language English
    Publishing date 2023-09-18
    Publishing country United States
    Document type Journal Article
    ZDB-ID 2844562-4
    ISSN 2470-0053 ; 2470-0045
    ISSN (online) 2470-0053
    ISSN 2470-0045
    DOI 10.1103/PhysRevE.108.024203
    Database MEDical Literature Analysis and Retrieval System OnLINE

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