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Detection of deterministic and chaotic signals on the basis of the LSTM model training results.
IF 2.7 2区 数学
Chaos Pub Date : 2025-03-01 DOI: 10.1063/5.0224768
Pawel Kasprowski, Dariusz Augustyn, Agnieszka Szczęsna, Henryk Josiński, Katarzyna Harężlak, Adam Świtoński
{"title":"Detection of deterministic and chaotic signals on the basis of the LSTM model training results.","authors":"Pawel Kasprowski, Dariusz Augustyn, Agnieszka Szczęsna, Henryk Josiński, Katarzyna Harężlak, Adam Świtoński","doi":"10.1063/5.0224768","DOIUrl":"https://doi.org/10.1063/5.0224768","url":null,"abstract":"<p><p>Detection of chaos in dynamical signals is an important and popular research area. Traditionally, the chaotic behavior is evaluated by calculating the Largest Lyapunov Exponent (LLE). However, calculating the LLE is sometimes difficult and requires specific data. Moreover, it introduces some subjective assumptions and is sometimes called a \"manual\" method. Therefore, there are many attempts to provide alternative ways to assess the dynamical signal as chaotic or deterministic. Some of them use deep learning methods. In this paper, we present a novel method of signal classification that is based on the assumption that it is easier to learn deterministic behavior than a chaotic one. We show that based on this assumption, it is possible to calculate the \"amount of chaos\" in the signal with the help of a simple LSTM (Long Short-Term Memory) neural network. The main advantage of this method is that-contrary to other deep learning-based methods-it does not require prior data to train the network as the results of the training process for a signal being classified are taken into account as the result of this evaluation. We confirm the method's validity using the publicly available dataset of chaotic and deterministic signals.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143699875","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
Beyond the bifurcation scenarios in vertical-cavity surface-emitting lasers with optical injection.
IF 2.7 2区 数学
Chaos Pub Date : 2025-03-01 DOI: 10.1063/5.0239988
Gonzalo Marcelo Ramírez-Ávila, Timoteo Carletti
{"title":"Beyond the bifurcation scenarios in vertical-cavity surface-emitting lasers with optical injection.","authors":"Gonzalo Marcelo Ramírez-Ávila, Timoteo Carletti","doi":"10.1063/5.0239988","DOIUrl":"https://doi.org/10.1063/5.0239988","url":null,"abstract":"<p><p>We study the dynamic behavior in a vertical-cavity surface-emitting laser subject to orthogonal optical injection through the computation of Lyapunov exponents and isospikes for a wide range of intervals in the plane of the injection parameters, i.e., the frequency detuning vs injection strength plane. Our thorough numerical experiments on this plane constitute a deep quantitative analysis of the different bifurcation scenarios leading to polarization switching (PS). First, we obtain similar results for the linearly polarized intensities for the different PS scenarios, especially when the injection strength is increased. It allows us to determine the parameter values that will be used for further analysis of the bifurcation scenarios in the parameter space. Analysis of different phase diagrams enables us to show multistability in the system and identify in the parameter planes several regions such as the predominantly chaotic lobe ones inside them are embedded some mainly regular structures such as spirals, rings, tricorns, shrimp networks, \"eye(s) of chaos,\" and chiral and nonchiral distribution of periodicities characterized by sequences of quint points. We emphasize two routes to chaos, namely, period-doubling and quint-point-based bifurcations.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143669180","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
Bifurcations and collective states of Kuramoto oscillators with higher-order interactions and rotational symmetry breaking.
IF 2.7 2区 数学
Chaos Pub Date : 2025-03-01 DOI: 10.1063/5.0239017
Antonio Mihara, Célia M Kuwana, Roberto C Budzinski, Lyle E Muller, Rene O Medrano-T
{"title":"Bifurcations and collective states of Kuramoto oscillators with higher-order interactions and rotational symmetry breaking.","authors":"Antonio Mihara, Célia M Kuwana, Roberto C Budzinski, Lyle E Muller, Rene O Medrano-T","doi":"10.1063/5.0239017","DOIUrl":"https://doi.org/10.1063/5.0239017","url":null,"abstract":"<p><p>We study a network of identical Kuramoto oscillators with higher-order interactions that also break the rotational symmetry of the system. To gain analytical insights into this model, we use the Watanabe-Strogatz Ansatz, which allows us to reduce the dimensionality of the original system of equations. The study of stability and bifurcations of the reduced system reveals a codimension two Bogdanov-Takens bifurcation and several other associated bifurcations. Such analysis is corroborated by numerical simulations of the associated Kuramoto system, which, in turn, unveils a variety of collective behaviors such as synchronized motion, oscillation death, chimeras, incoherent states, and traveling waves. Importantly, this system displays a case where alternating chimeras emerge in an indistinguishable single population of oscillators, which may offer insights into the unihemispheric slow-wave sleep phenomenon observed in mammals and birds.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143630217","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
Analyzing deterministic and stochastic influences on the power grid frequency dynamics with explainable artificial intelligence.
IF 2.7 2区 数学
Chaos Pub Date : 2025-03-01 DOI: 10.1063/5.0239371
Tim Drewnick, Xinyi Wen, Ulrich Oberhofer, Leonardo Rydin Gorjão, Christian Beck, Veit Hagenmeyer, Benjamin Schäfer
{"title":"Analyzing deterministic and stochastic influences on the power grid frequency dynamics with explainable artificial intelligence.","authors":"Tim Drewnick, Xinyi Wen, Ulrich Oberhofer, Leonardo Rydin Gorjão, Christian Beck, Veit Hagenmeyer, Benjamin Schäfer","doi":"10.1063/5.0239371","DOIUrl":"https://doi.org/10.1063/5.0239371","url":null,"abstract":"<p><p>Power grids are essential for our society, connecting consumers and generators. Their frequency stability is impacted by supply and demand changes, including deterministic and stochastic dynamics, e.g., from market activities or fluctuating renewables. The first two Kramers-Moyal coefficients allow for a description of both the deterministic (via drift) and stochastic (via diffusion) aspects of these dynamics. Such a description and understanding could be critical to stabilizing power systems. However, how drift and diffusion differ between synchronous areas, how they vary over time, and how the generation mix influences them, remains unclear. Analyzing temporal patterns in drift and diffusion for frequency data from Australia (AUS) and Continental Europe (CE), we reveal a positive correlation between drift and diffusion. In addition, we utilize both gradient-boosted trees and neural network models to train drift and diffusion models for AUS and CE. Shapley additive explanations make these black-box models transparent and allow us to identify the total generation and load to influence the drift, while calendar features seem critical for the diffusion coefficient estimates.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143699749","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
Chaos in a class of piecewise nonlinear systems with homoclinic cycles.
IF 2.7 2区 数学
Chaos Pub Date : 2025-03-01 DOI: 10.1063/5.0246243
Kai Lu, Wenjing Xu
{"title":"Chaos in a class of piecewise nonlinear systems with homoclinic cycles.","authors":"Kai Lu, Wenjing Xu","doi":"10.1063/5.0246243","DOIUrl":"https://doi.org/10.1063/5.0246243","url":null,"abstract":"<p><p>It is still a challenge to accurately predict homoclinic cycles and chaos in smooth nonlinear systems, letting alone for non-smooth objects. This paper analytically investigates occurrence of homoclinic cycles in a class of three-dimensional piecewise nonlinear systems governed by a nonlinear subsystem and an affine one, which under some conditions can be transformed into a linear form. By a series of equivalent transformations, the solution of the considered systems can be obtained explicitly. Furthermore, via deriving analytic expression of Poincaré return maps, it rigorously proves that the considered system presents complicated chaotic dynamics. This approach offers a way to identify singular cycles and chaos in other piecewise systems exhibiting nonlinearities. Two examples are provided finally to numerically illustrate and verify effectiveness of our theoretical results established.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143673384","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
The role of solar heat in earthquake activity.
IF 2.7 2区 数学
Chaos Pub Date : 2025-03-01 DOI: 10.1063/5.0243721
Matheus Henrique Junqueira Saldanha, Masanori Shiro, Yuji Yagi, Yoshito Hirata
{"title":"The role of solar heat in earthquake activity.","authors":"Matheus Henrique Junqueira Saldanha, Masanori Shiro, Yuji Yagi, Yoshito Hirata","doi":"10.1063/5.0243721","DOIUrl":"https://doi.org/10.1063/5.0243721","url":null,"abstract":"<p><p>We have shown, in a previous work, that the solar activity causally influences earthquake activity on Earth [M. H. Junqueira Saldanha and Y. Hirata, Chaos 32, 061107 (2022)]. However, the mechanisms by which the Sun can affect seismic activity on Earth are still unknown. Here, we examine the hypothesis that one of such influences is through heat. To support this, we present a diverse array of evidence, including the existence of variation in Earth's seismicity throughout the different seasons; the presence of shared dynamical information and a large degree of non-determinism in solar activity and earthquakes; an increase in earthquake predictability if surface atmospheric temperature is considered an independent variable; and a variation in such predictability when accounting for a delayed sunspot time series, which aligns with the expected timescales of heat transfer and its effects on Earth's systems.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143540289","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
The origin of localized patterns with a spatiotemporal oscillatory background state.
IF 2.7 2区 数学
Chaos Pub Date : 2025-03-01 DOI: 10.1063/5.0249873
Zhi-Chao Xue, Li Li
{"title":"The origin of localized patterns with a spatiotemporal oscillatory background state.","authors":"Zhi-Chao Xue, Li Li","doi":"10.1063/5.0249873","DOIUrl":"https://doi.org/10.1063/5.0249873","url":null,"abstract":"<p><p>The localized patterns observed with a spatiotemporal oscillatory background in the experiment are believed to emerge due to the bistability of supercritical Turing-Hopf modes. However, the branching origin of these patterns remains unclear. In this paper, we explore the formation of local patterns near the subcritical Turing-Hopf bifurcation point using the Gray-Scott model as an example. By employing the multiple scales analysis method, we derive the amplitude equation coupling both time and space, demonstrating that this special localized pattern can persist even under a subcritical bifurcation. Through numerical continuation and bifurcation analysis, we reveal that the patterns originate from a new branch on the homoclinic snaking. Our findings provide new insights into the formation of complex spatiotemporal patterns and offer a reasonable explanation for the origin of oscillatory localized patterns from the perspective of higher-order bifurcations.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143604073","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
Cantor subsystems on the Gehman dendrite.
IF 2.7 2区 数学
Chaos Pub Date : 2025-03-01 DOI: 10.1063/5.0249144
Piotr Oprocha, Jakub Tomaszewski
{"title":"Cantor subsystems on the Gehman dendrite.","authors":"Piotr Oprocha, Jakub Tomaszewski","doi":"10.1063/5.0249144","DOIUrl":"https://doi.org/10.1063/5.0249144","url":null,"abstract":"<p><p>In the present paper, we focus on dynamical systems on the Gehman dendrite G. It is well-known that the set of end points of this dendrite is homeomorphic to the standard Cantor ternary set C. For any given surjective dynamical system acting on C, we provide constructions of dynamical systems on G, which are (i) topologically mixing but not exact or (ii) topologically exact, and such that in both cases, the subsystem acting on the set of end points End(G) is conjugate to the initially chosen dynamical system on C.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143603847","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
Influence maximization in multilayer networks based on adaptive coupling degree.
IF 2.7 2区 数学
Chaos Pub Date : 2025-03-01 DOI: 10.1063/5.0256704
Su-Su Zhang, Ming Xie, Chuang Liu, Xiu-Xiu Zhan
{"title":"Influence maximization in multilayer networks based on adaptive coupling degree.","authors":"Su-Su Zhang, Ming Xie, Chuang Liu, Xiu-Xiu Zhan","doi":"10.1063/5.0256704","DOIUrl":"https://doi.org/10.1063/5.0256704","url":null,"abstract":"<p><p>Influence maximization (IM) aims to identify highly influential nodes to maximize influence spread in a network. Previous research on the IM problem has mainly concentrated on single-layer networks, disregarding the comprehension of the coupling structure that is inherent in multilayer networks. To solve the IM problem in multilayer networks, we first propose an independent cascade model (MIC) in a multilayer network where propagation occurs simultaneously across different layers. Consequently, a heuristic algorithm, i.e., adaptive coupling degree (ACD), which selects seed nodes with high spread influence and a low degree of overlap of influence, is proposed to identify seed nodes for IM in a multilayer network. By conducting experiments based on MIC, we have demonstrated that our proposed method is superior to the baselines in terms of influence spread and time cost in six synthetic and four real-world multilayer networks.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143630221","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
Chaos analyses of visco-hyperelastic cylindrical shells based on improved Melnikov method. 基于改进的梅尔尼科夫方法的粘弹性圆柱壳混沌分析。
IF 2.7 2区 数学
Chaos Pub Date : 2025-03-01 DOI: 10.1063/5.0253278
Ran Wang, Ming E Yin, Zhentao Zhao
{"title":"Chaos analyses of visco-hyperelastic cylindrical shells based on improved Melnikov method.","authors":"Ran Wang, Ming E Yin, Zhentao Zhao","doi":"10.1063/5.0253278","DOIUrl":"https://doi.org/10.1063/5.0253278","url":null,"abstract":"<p><p>Soft-material structures have excellent characteristics of infinite degrees of freedom and large deformation, and it has important theoretical significance and application value to perform mathematical modeling and dynamic analysis. This paper studies the large-amplitude oscillation of the cylindrical shell under a harmonic excitation, where the constitutive relationship is described by the Zener rheological model based on the Rivlin-Saunders hyperelastic model. First, the Euler Lagrange equation is used to establish the nonlinear ordinary differential equation describing the radially symmetric motion of the structure, and the viscous evolution equation of the material is derived based on the rheological model, thus obtaining the governing equations of the nonlinear system. Second, based on the zero-viscosity and infinite-viscosity models, the bifurcation behaviors and natural frequency analyses of the nonlinear dynamics of thin-walled structures under constant loads are carried out. Third, based on the small perturbation assumption of the Maxwell unit, an improved Melnikov method suitable for the dynamic analysis of the visco-hyperelastic shells under harmonic excitation is proposed and verified by numerical methods. Finally, the chaos threshold of the system is analyzed based on the improved Melnikov method.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143630218","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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