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Generalized synchronization in the presence of dynamical noise and its detection via recurrent neural networks.
IF 2.7 2区 数学
Chaos Pub Date : 2024-12-01 DOI: 10.1063/5.0235802
José M Amigó, Roberto Dale, Juan C King, Klaus Lehnertz
{"title":"Generalized synchronization in the presence of dynamical noise and its detection via recurrent neural networks.","authors":"José M Amigó, Roberto Dale, Juan C King, Klaus Lehnertz","doi":"10.1063/5.0235802","DOIUrl":"https://doi.org/10.1063/5.0235802","url":null,"abstract":"<p><p>Given two unidirectionally coupled nonlinear systems, we speak of generalized synchronization when the responder \"follows\" the driver. Mathematically, this situation is implemented by a map from the driver state space to the responder state space termed the synchronization map. In nonlinear times series analysis, the framework of the present work, the existence of the synchronization map amounts to the invertibility of the so-called cross map, which is a continuous map that exists in the reconstructed state spaces for typical time-delay embeddings. The cross map plays a central role in some techniques to detect functional dependencies between time series. In this paper, we study the changes in the \"noiseless scenario\" just described when noise is present in the driver, a more realistic situation that we call the \"noisy scenario.\" Noise will be modeled using a family of driving dynamics indexed by a finite number of parameters, which is sufficiently general for practical purposes. In this approach, it turns out that the cross and synchronization maps can be extended to the noisy scenario as families of maps that depend on the noise parameters, and only for \"generic\" driver states in the case of the cross map. To reveal generalized synchronization in both the noiseless and noisy scenarios, we check the existence of synchronization maps of higher periods (introduced in this paper) using recurrent neural networks and predictability. The results obtained with synthetic and real-world data demonstrate the capability of our method.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142845804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Particle transport in open polygonal billiards: A scattering map.
IF 2.7 2区 数学
Chaos Pub Date : 2024-12-01 DOI: 10.1063/5.0219730
Jordan Orchard, Federico Frascoli, Lamberto Rondoni, Carlos Mejía-Monasterio
{"title":"Particle transport in open polygonal billiards: A scattering map.","authors":"Jordan Orchard, Federico Frascoli, Lamberto Rondoni, Carlos Mejía-Monasterio","doi":"10.1063/5.0219730","DOIUrl":"https://doi.org/10.1063/5.0219730","url":null,"abstract":"<p><p>Polygonal billiards exhibit a rich and complex dynamical behavior. In recent years, polygonal billiards have attracted much attention due to their application in the understanding of anomalous transport, but also at the fundamental level, due to their connections with diverse fields in mathematics. We explore this complexity and its consequences on the properties of particle transport in infinitely long channels made of the repetitions of an elementary open polygonal cell. Borrowing ideas from the Zemlyakov-Katok construction, we construct an interval exchange transformation classified by the singular directions of the discontinuities of the billiard flow over the translation surface associated with the elementary cell. From this, we derive an exact expression of a scattering map of the cell connecting the outgoing flow of trajectories with the unconstrained incoming flow. The scattering map is defined over a partition of the coordinate space, characterized by different families of trajectories. Furthermore, we obtain an analytical expression for the average speed of propagation of ballistic modes, describing with high accuracy the speed of propagation of ballistic fronts appearing in the tails of the distribution of the particle displacement. The symbolic hierarchy of the trajectories forming these ballistic fronts is also discussed.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142845822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Complexity measure of extreme events.
IF 2.7 2区 数学
Chaos Pub Date : 2024-12-01 DOI: 10.1063/5.0232645
Dhiman Das, Arnob Ray, Chittaranjan Hens, Dibakar Ghosh, Md Kamrul Hassan, Artur Dabrowski, Tomasz Kapitaniak, Syamal K Dana
{"title":"Complexity measure of extreme events.","authors":"Dhiman Das, Arnob Ray, Chittaranjan Hens, Dibakar Ghosh, Md Kamrul Hassan, Artur Dabrowski, Tomasz Kapitaniak, Syamal K Dana","doi":"10.1063/5.0232645","DOIUrl":"https://doi.org/10.1063/5.0232645","url":null,"abstract":"<p><p>Complexity is an important metric for appropriate characterization of different classes of irregular signals, observed in the laboratory or in nature. The literature is already rich in the description of such measures using a variety of entropy and disequilibrium measures, separately or in combination. Chaotic signal was given prime importance in such studies while no such measure was proposed so far, how complex were the extreme events when compared to non-extreme chaos. We address here this question of complexity in extreme events and investigate if we can distinguish them from non-extreme chaotic signal. The normalized Shannon entropy in combination with disequilibrium is used for our study and it is able to distinguish between extreme chaos and non-extreme chaos and moreover, it depicts the transition points from periodic to extremes via Pomeau-Manneville intermittency and, from small amplitude to large amplitude chaos and its transition to extremes via interior crisis. We report a general trend of complexity against a system parameter that increases during a transition to extreme events, reaches a maximum, and then starts decreasing. We employ three models, a nonautonomous Liénard system, two-dimensional Ikeda map and a six-dimensional coupled Hindmarsh-Rose system to validate our proposition.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142766732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Finding Birkhoff averages via adaptive filtering.
IF 2.7 2区 数学
Chaos Pub Date : 2024-12-01 DOI: 10.1063/5.0215396
M Ruth, D Bindel
{"title":"Finding Birkhoff averages via adaptive filtering.","authors":"M Ruth, D Bindel","doi":"10.1063/5.0215396","DOIUrl":"https://doi.org/10.1063/5.0215396","url":null,"abstract":"<p><p>In many applications, one is interested in classifying trajectories of symplectic maps as invariant tori, islands, or chaos. Here, we introduce Birkhoff reduced rank extrapolation (RRE), a modified version of the RRE method, which efficiently obtains ergodic averages of invariant tori and islands in symplectic maps. In contrast, Birkhoff RRE does not efficiently converge in chaos, meaning its convergence rate can be used for trajectory classification. Furthermore, for the islands and invariant circles, Birkhoff RRE returns the number of islands and the rotation number. This allows us to find Fourier parameterizations of invariant circles and islands from a single trajectory. We show examples of Birkhoff RRE on the standard map and magnetic field line dynamics.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142766792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Shrimp structure as a test bed for ordinal pattern measures. 将虾结构作为序数模式测量的试验台。
IF 2.7 2区 数学
Chaos Pub Date : 2024-12-01 DOI: 10.1063/5.0238632
Yong Zou, Norbert Marwan, Xiujing Han, Reik V Donner, Jürgen Kurths
{"title":"Shrimp structure as a test bed for ordinal pattern measures.","authors":"Yong Zou, Norbert Marwan, Xiujing Han, Reik V Donner, Jürgen Kurths","doi":"10.1063/5.0238632","DOIUrl":"https://doi.org/10.1063/5.0238632","url":null,"abstract":"<p><p>Identifying complex periodic windows surrounded by chaos in the two or higher dimensional parameter space of certain dynamical systems is a challenging task for time series analysis based on complex network approaches. This holds particularly true for the case of shrimp structures, where different bifurcations occur when crossing different domain boundaries. The corresponding dynamics often exhibit either period-doubling when crossing the inner boundaries or, respectively, intermittency for outer boundaries. Numerically characterizing especially the period-doubling route to chaos is difficult for most existing complex network based time series analysis approaches. Here, we propose to use ordinal pattern transition networks (OPTNs) to characterize shrimp structures, making use of the fact that the transition behavior between ordinal patterns encodes additional dynamical information that is not captured by traditional ordinal measures such as permutation entropy. In particular, we compare three measures based on ordinal patterns: traditional permutation entropy εO, average amplitude fluctuations of ordinal patterns ⟨σ⟩, and OPTN out-link transition entropy εE. Our results demonstrate that among those three measures, εE performs best in distinguishing chaotic from periodic time series in terms of classification accuracy. Therefore, we conclude that transition frequencies between ordinal patterns encoded in the OPTN link weights provide complementary perspectives going beyond traditional methods of ordinal time series analysis that are solely based on pattern occurrence frequencies.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142845832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mitigating epidemic spread in complex networks based on deep reinforcement learning.
IF 2.7 2区 数学
Chaos Pub Date : 2024-12-01 DOI: 10.1063/5.0235689
Jie Yang, Wenshuang Liu, Xi Zhang, Choujun Zhan
{"title":"Mitigating epidemic spread in complex networks based on deep reinforcement learning.","authors":"Jie Yang, Wenshuang Liu, Xi Zhang, Choujun Zhan","doi":"10.1063/5.0235689","DOIUrl":"https://doi.org/10.1063/5.0235689","url":null,"abstract":"<p><p>Complex networks are susceptible to contagious cascades, underscoring the urgency for effective epidemic mitigation strategies. While physical quarantine is a proven mitigation measure for mitigation, it can lead to substantial economic repercussions if not managed properly. This study presents an innovative approach to selecting quarantine targets within complex networks, aiming for an efficient and economic epidemic response. We model the epidemic spread in complex networks as a Markov chain, accounting for stochastic state transitions and node quarantines. We then leverage deep reinforcement learning (DRL) to design a quarantine strategy that minimizes both infection rates and quarantine costs through a sequence of strategic node quarantines. Our DRL agent is specifically trained with the proximal policy optimization algorithm to optimize these dual objectives. Through simulations in both synthetic small-world and real-world community networks, we demonstrate the efficacy of our strategy in controlling epidemics. Notably, we observe a non-linear pattern in the mitigation effect as the daily maximum quarantine scale increases: the mitigation rate is most pronounced at first but plateaus after reaching a critical threshold. This insight is crucial for setting the most effective epidemic mitigation parameters.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142863508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Critical threshold for synchronizability of high-dimensional Kuramoto oscillators under higher-order interactions.
IF 2.7 2区 数学
Chaos Pub Date : 2024-12-01 DOI: 10.1063/5.0211410
Hyungjin Huh, Dohyun Kim
{"title":"Critical threshold for synchronizability of high-dimensional Kuramoto oscillators under higher-order interactions.","authors":"Hyungjin Huh, Dohyun Kim","doi":"10.1063/5.0211410","DOIUrl":"https://doi.org/10.1063/5.0211410","url":null,"abstract":"<p><p>We study the asymptotic dynamics of the high-dimensional Kuramoto oscillators on the unit sphere with two- and three-body interactions that trigger competition between synchrony and non-synchrony. In this work, we find a critical threshold between interaction strengths for complete synchronizability. Moreover, critical slowing down is observed at this phase transition. Our main theorems are supplemented by several numerical experiments, which provide a qualitative insight beyond theoretical results.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142766735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Effects of value-driven social learning on cooperation in the prisoner's dilemma games.
IF 2.7 2区 数学
Chaos Pub Date : 2024-12-01 DOI: 10.1063/5.0242023
Haojie Xu, Hongshuai Wu, Changwei Huang
{"title":"Effects of value-driven social learning on cooperation in the prisoner's dilemma games.","authors":"Haojie Xu, Hongshuai Wu, Changwei Huang","doi":"10.1063/5.0242023","DOIUrl":"https://doi.org/10.1063/5.0242023","url":null,"abstract":"<p><p>Despite the growing attention and research on the impact of Q-learning-based strategy updating on the evolution of cooperation, the joint role of individual learners and social learners in evolutionary games has seldom been considered. Here, we propose a value-driven social learning model that incorporates a shape parameter, β, to characterize the degree of radicalism or conservatism in social learning. Using the prisoner's dilemma game on a square lattice as a paradigm, our simulation results show that the cooperation level has a non-trivial dependence of β, density ρ, and dilemma strength b. We find that both β and ρ have nonmonotonic effects on cooperation; specifically, moderate levels of radicalism in social learning can facilitate cooperation remarkably, and when slightly conservative, can form a favorable cooperation region with the appropriate ρ. Moreover, we have demonstrated that social learners play a key role in the formation of network reciprocity, whereas individual learners play a dual role of support and exploitation. Our results reveal a critical balance between individual learning and social learning that can maximize cooperation and provide insights into understanding the collective behavior in multi-agent systems.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142766742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Network structure and time delays shape synchronization patterns in brain network models.
IF 2.7 2区 数学
Chaos Pub Date : 2024-12-01 DOI: 10.1063/5.0228813
Iain Pinder, Martin R Nelson, Jonathan J Crofts
{"title":"Network structure and time delays shape synchronization patterns in brain network models.","authors":"Iain Pinder, Martin R Nelson, Jonathan J Crofts","doi":"10.1063/5.0228813","DOIUrl":"https://doi.org/10.1063/5.0228813","url":null,"abstract":"<p><p>In this paper, we investigate synchronization patterns and coherence for a network of delayed Wilson-Cowan nodes. To capture information processing across different brain regions, our model incorporates two distinct delays: an intra-nodal delay that reflects the time signals take to travel within a cortical region due to local circuitry and an inter-nodal delay representing the longer communication times associated with white matter connections between brain areas. To investigate the role of network topology, we consider a range of toy network structures as well as the known (macro-scale) cortical structure of the Macaque monkey. We examine how global network dynamics are shaped by a combination of network configuration, coupling strength, and time delays. Our focus lies on two dynamic measures: synchrony and metastability, the latter reflecting the temporal variation of the former, both crucial for the brain's real-time functionality. Our investigation identifies extensive regions within the system's parameter space where the synchronized state exhibits transverse instabilities. These instabilities give rise to diverse dynamical behaviors contingent upon the network architecture and the interplay between coupling strength and time delay. While similar complex partially synchronized states existed for all network topologies considered, the cortical network demonstrated time-dependent behaviors, such as phase cluster dynamics, which were absent in the toy network architectures, and which are considered crucial in its ability to orchestrate complex information processing and behavior. Additionally, we illustrate how delays can regulate a cortical network with chaotic local dynamics, thus emphasizing the potential importance of delays in suppressing pathological spreading dynamics.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142766850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Parrondo's effects with aperiodic protocols.
IF 2.7 2区 数学
Chaos Pub Date : 2024-12-01 DOI: 10.1063/5.0233604
Marcelo A Pires, Erveton P Pinto, Rone N da Silva, Sílvio M Duarte Queirós
{"title":"Parrondo's effects with aperiodic protocols.","authors":"Marcelo A Pires, Erveton P Pinto, Rone N da Silva, Sílvio M Duarte Queirós","doi":"10.1063/5.0233604","DOIUrl":"https://doi.org/10.1063/5.0233604","url":null,"abstract":"<p><p>In this work, we study the effectiveness of employing archetypal aperiodic sequencing-namely, Fibonacci, Thue-Morse, and Rudin-Shapiro-on the Parrondian effect. From a capital gain perspective, our results show that these series do yield a Parrondo's paradox with the Thue-Morse based strategy outperforming not only the other two aperiodic strategies but benchmark Parrondian games with random and periodical (AABBAABB…) switching as well. The least performing of the three aperiodic strategies is the Rudin-Shapiro. To elucidate the underlying causes of these results, we analyze the cross correlation between the capital generated by the switching protocols and that of the isolated losing games. This analysis reveals that a strong anticorrelation with both isolated games is typically required to achieve a robust manifestation of Parrondo's effect. We also study the influence of the sequencing on the capital using the lacunarity and persistence measures. In general, we observe that the switching protocols tend to become less performing in terms of the capital as one increases the persistence and, thus, approaches the features of an isolated losing game. For the (log-)lacunarity, a property related to heterogeneity, we notice that for small persistence (less than 0.5), the performance increases with the lacunarity with a maximum around 0.4. In respect of this, our work shows that the optimization of a switching protocol is strongly dependent on a fine-tuning between persistence and heterogeneity.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142779173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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