IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0337970

Byeongchan Choi, Junwon You, Myung Ock Kim, Jae-Hun Jung

{"title":"Zipf-Mandelbrot scaling in Korean court music: Universal patterns in music.","authors":"Byeongchan Choi, Junwon You, Myung Ock Kim, Jae-Hun Jung","doi":"10.1063/5.0337970","DOIUrl":"10.1063/5.0337970","url":null,"abstract":"Rank-frequency distributions in many complex systems, including natural language, are often well described by the Zipf-Mandelbrot law. Due to the semantic characteristics of this law, it has also been observed in musical data. However, most such studies have focused on Western music, and its applicability to non-Western music remains not well investigated. We analyzed 43 Korean court music pieces called Jeong-ak, spanning several centuries and written in the traditional Korean musical notation Jeongganbo. These pieces were transcribed into Western staff notation, and musical data such as pitch and duration were extracted. Using pitch, duration, and their paired combinations as Zipfian units, we found that Korean music also fits the Zipf-Mandelbrot law to a high degree, particularly for the paired pitch-duration unit. Korean music has evolved collectively over long periods, smoothing idiosyncratic variations and producing forms that are widely understandable among people. This collective evolution appears to have played a significant role in shaping the characteristics that lead to the satisfaction of Zipf-Mandelbrot law. Our findings provide additional evidence that Zipf-Mandelbrot scaling in musical data is universal across cultures. We further show that the joint distribution of two independent Zipfian data sets follows the Zipf-Mandelbrot law.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 9","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148918391","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

Amplified topic coupling and polarization by higher-order interactions in multidimensional opinion dynamics. 多维意见动态中的高阶互动放大了话题耦合和极化。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0337453

Bingchen Dong, Qiang Zhang, Zhenglin Liang

{"title":"Amplified topic coupling and polarization by higher-order interactions in multidimensional opinion dynamics.","authors":"Bingchen Dong, Qiang Zhang, Zhenglin Liang","doi":"10.1063/5.0337453","DOIUrl":"https://doi.org/10.1063/5.0337453","url":null,"abstract":"Online discussions often exhibit multidimensional polarization, in which stances on distinct topics become aligned along broader ideological dimensions. Analysis of Reddit data indicates that this cross-topic stance coupling appears within co-participating discussion groups. Motivated by this observation, we introduce a multidimensional opinion dynamics model on a two-layer structure with pairwise edges and hyperedges, together with a group conformity exponent that controls nonlinear group influence. Mean-field and bifurcation analyses reveal two dynamical mechanisms. Linear group conformity lowers the critical threshold at which neutral consensus loses stability and increases cross-topic coupling. Nonlinear group conformity leaves this threshold unchanged but introduces a subcritical bifurcation with a bistable regime. Empirical analysis of data from 27 subreddits spanning four ideological dimensions provides supporting evidence for these mechanisms and shows that the proposed model more closely reproduces observed polarization and coupling patterns than several benchmarks. These results highlight the role of group structures in shaping collective opinion dynamics on online platforms and may offer potential insights for platform governance.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 9","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148879250","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

In memoriam-Kenneth Showalter (9 April 1949-4 June 2026). kenneth Showalter（1949年4月9日- 2026年6月4日）

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0350230

Oliver Steinbock, Mark Tinsley, Ágota Tóth, Dezső Horváth

引用次数: 0

Continuously pleated torus or strange nonchaotic attractors seen as continuously fractalized quasiperiodic attractors. 连续褶皱环面或奇异非混沌吸引子视为连续分形准周期吸引子。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0354681

Christophe Letellier, Nataliya Stankevich, Samer Houri, Ludovico Minati

{"title":"Continuously pleated torus or strange nonchaotic attractors seen as continuously fractalized quasiperiodic attractors.","authors":"Christophe Letellier, Nataliya Stankevich, Samer Houri, Ludovico Minati","doi":"10.1063/5.0354681","DOIUrl":"https://doi.org/10.1063/5.0354681","url":null,"abstract":"Toroidal chaos designates a chaotic solution that is structured in the neighborhood of a torus. For being chaotic, such a torus needs to be discontinuously fractalized to present a Cantor set, ensuring the great sensitivity to initial conditions required for chaos. A fractal is related to self-similarity and a non-integer dimension. In fact, although clearly introduced as such by Mandelbrot, it was never written in a paper related to strange nonchaotic attractors that an object can be fractal in two very different ways: under a continuous way, as a coastline, or in a discontinuous way, as a Cantor set. If the latter is necessarily related to chaos, the former can, for instance, be associated with a continuous torus fractalization leading to a strange nonchaotic attractor. Moreover, although being fractal, the torus is still regular and, consequently, a strange nonchaotic attractor is a particular type of quasiperiodic attractor. We will, therefore, focus on showing with the help of three different cases-produced by two coupled van der Pol oscillators or by a quasiperiodically driven Duffing system, that the fractalization is actually continuous when strange nonchaotic attractors are observed. In one of the cases, it will be shown that the largest Lyapunov exponent wrongly suggests chaos rather than a strange nonchaotic attractor. We also investigate how, in the presence of symmetry, an attractor merging crisis-induced intermittency can be observed, just after two symmetry-related strange nonchaotic attractors.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 9","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148966924","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

Latent factors capturing evolution of behavior in larval zebrafish. 捕获斑马鱼幼虫行为进化的潜在因素。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0354035

Changhong Han, Yuchen Gong, Le Sun, Jiulin Du, Peng Ji

{"title":"Latent factors capturing evolution of behavior in larval zebrafish.","authors":"Changhong Han, Yuchen Gong, Le Sun, Jiulin Du, Peng Ji","doi":"10.1063/5.0354035","DOIUrl":"https://doi.org/10.1063/5.0354035","url":null,"abstract":"Animal behavior exhibits remarkable diversity across spatial and temporal scales, showing both significant regularity and high variability. Understanding such multiscale dynamics is essential for revealing the mechanisms and organizing principles that generate behavior and shape motor control. However, conventional analyses largely rely on static or statistical descriptors, which fail to capture the intrinsic dynamical rules governing behavioral evolution over time. Larval zebrafish, whose body posture can be quantified as spatial coordinates, provide an ideal vertebrate model for studying behavioral dynamics. Here, we develop a dynamical reconstruction framework that combines delay embedding with an echo state network to recover the latent state space of zebrafish behavior from high-dimensional postural time series. The framework preserves temporal dependencies and maps postural variations onto latent factors whose combinations define distinct behavioral states-turning, routine swimming, and slow swimming-matching feature-based clustering. These states evolve as continuous trajectories on a low-dimensional attractor, with transitions marked by nonlinear tipping points that reflect reorganization of underlying factors. Leveraging this reconstructed state space, the framework also enables short-term behavioral prediction. Overall, our framework provides a unified quantitative tool for revealing the latent dynamical principles of zebrafish behavior, with potential extensions to neural and bio-inspired control.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 9","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149073684","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

Nonmonotonic reorganization of excitation and relaxation in multidimensional excitable media. 多维可激介质中激发和弛豫的非单调重组。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0348139

Slobodanka Galovic, Zoran Ivic, Dalibor Chevizovich, Giorgos P Tsironis

{"title":"Nonmonotonic reorganization of excitation and relaxation in multidimensional excitable media.","authors":"Slobodanka Galovic, Zoran Ivic, Dalibor Chevizovich, Giorgos P Tsironis","doi":"10.1063/5.0348139","DOIUrl":"https://doi.org/10.1063/5.0348139","url":null,"abstract":"We analyze excitation and relaxation dynamics in a two-dimensional heterogeneous excitable medium described by a smoothly regularized three-variable Fenton-Karma model. To relate spatial heterogeneity to a global observable, we examine the dipole response together with the evolution of two activation-threshold manifolds associated with distinct regimes of the excitation-relaxation dynamics of the model. We show that increasing diffusion contrast does not produce a monotonic change in the global excitation-relaxation organization. For weak contrast, excitation remains globally connected despite deformation of the excitation pattern. For intermediate contrast, the system fails to establish a globally connected excited state outside the heterogeneous region, leading to the disappearance of the characteristic negative T-wave-like minimum in the dipole signal. However, a further increase in diffusion contrast restores global connectivity despite the persistence of a trapped low-potential region within the heterogeneity. These results demonstrate that localized heterogeneity can induce a nonmonotonic reorganization of excitation-relaxation dynamics by modifying the ability of the system to establish globally connected excitation. Simultaneously, the global dipole signal directly encodes transitions between regimes with and without a globally connected excited state.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 9","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148873232","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

Reciprocity-induced proliferation: Survival resonance and equilibrium beyond the tragedy of the commons. 互惠诱导的扩散：超越公地悲剧的生存共振与平衡。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0355088

Yi-Duo Chen, Zhi-Xi Wu, Jian-Yue Guan

引用次数: 0

Social bonds and helping dynamics promote cooperation in nested group populations. 社会纽带和帮助动力促进了嵌套群体群体的合作。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0351165

Ji Quan, Xinyue Huang, Xianjia Wang

{"title":"Social bonds and helping dynamics promote cooperation in nested group populations.","authors":"Ji Quan, Xinyue Huang, Xianjia Wang","doi":"10.1063/5.0351165","DOIUrl":"https://doi.org/10.1063/5.0351165","url":null,"abstract":"Most studies on the evolution of cooperation focus on single-group settings, whereas real-world interactions often occur within nested group structures and are shaped by pre-existing social relationships. The coexistence of cross-level public-goods allocation, dynamically evolving social bonds, and heterogeneous helping responses creates multiple feedback channels, making the stability of cooperation dependent on both group structure and relationship dynamics. To address these limitations, this study develops a two-stage game model that incorporates social bonds to characterize relationship strength. A helping function is further constructed based on bond sensitivity, bond midpoint threshold, and helping response parameters, capturing how social bonds influence cooperative behavior. Simulation results demonstrate that strong social bonds significantly promote cooperation. When bond sensitivity and midpoint threshold are low, even weak bonds can trigger mutual assistance, facilitating bond accumulation and generating a positive feedback loop that reinforces cooperation. Increasing the helping response enhances the level of assistance, accelerates the formation of strong bonds, and substantially improves cooperation. In contrast, although a higher bond learning rate speeds up bond accumulation, its impact on cooperation remains limited. Furthermore, larger local group sizes amplify the positive effect of social bonds on cooperation. Overall, this study provides a novel theoretical perspective on the mechanisms underlying the maintenance of cooperation in nested group structures.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 9","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148975782","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

Efficient driver-node selection for pinning control via second-order perturbations. 基于二阶扰动的钉住控制的高效驱动节点选择。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0351619

Fatemeh Ghoreishian Amiri, Fahimeh Nazarimehr, Sajad Jafari, Matjaž Perc

{"title":"Efficient driver-node selection for pinning control via second-order perturbations.","authors":"Fatemeh Ghoreishian Amiri, Fahimeh Nazarimehr, Sajad Jafari, Matjaž Perc","doi":"10.1063/5.0351619","DOIUrl":"https://doi.org/10.1063/5.0351619","url":null,"abstract":"Driver-node selection is a fundamental problem in the pinning control of complex networks, where the aim is to identify a small set of nodes whose external control can most effectively steer the collective dynamics of the network. Driver nodes are typically selected sequentially, and greedy optimization serves as the standard benchmark for such sequential methods since it produces near-optimal node sets. However, this level of accuracy comes at a computational cost that becomes prohibitive for large networks. In this work, we propose a second-order perturbation framework that overcomes this limitation by estimating the shift in the smallest eigenvalue of the network Laplacian, the quantity that governs the stability of the pinned network, using second-order perturbation theory. Consequently, the proposed method reduces the computational complexity of driver-node selection from O(N5) in conventional greedy schemes to O(N4), enabling efficient and scalable selection in large-scale networks. Extensive simulations across diverse network topologies, including small-world, scale-free, and random networks, demonstrate that the proposed method consistently outperforms standard centrality-based heuristics. It achieves performance comparable to optimal greedy benchmarks, while offering substantially higher computational efficiency. The proposed framework thus provides a practical and scalable solution for the control of large complex networks, and more broadly, demonstrates the utility of higher-order perturbation analysis for node-ranking problems in network controllability.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 9","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149069254","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

Learning the intrinsic dimensionality of Fermi-Pasta-Ulam-Tsingou trajectories: A nonlinear approach using a deep autoencoder model. 学习Fermi-Pasta-Ulam-Tsingou轨迹的内在维数：一种使用深度自编码器模型的非线性方法。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0335458

Gionni Marchetti

{"title":"Learning the intrinsic dimensionality of Fermi-Pasta-Ulam-Tsingou trajectories: A nonlinear approach using a deep autoencoder model.","authors":"Gionni Marchetti","doi":"10.1063/5.0335458","DOIUrl":"https://doi.org/10.1063/5.0335458","url":null,"abstract":"We address the intrinsic dimensionality (ID) of high-dimensional trajectories, comprising ns = 4 000 000 data points, generated by the Fermi-Pasta-Ulam-Tsingou (FPUT) β model with N = 32 oscillators. To this end, a deep autoencoder (DAE) is employed to infer the ID in the weakly nonlinear regime, where energy recurrences are observed (β≲1). Our results indicate that the trajectories lie on a two-dimensional Riemannian manifold (m* = 2) embedded in a 64-dimensional phase space. This finding is independently corroborated by a Fourier analysis of the time series associated with the normal mode coordinates and their corresponding energies, which reveals two independent frequencies, consistent with quasi-periodic motion on a two-dimensional invariant torus T2. By contrast, principal component analysis (PCA) can provide only a reasonable upper bound on the intrinsic dimensionality. Furthermore, the DAE predicts that the intrinsic dimensionality increases to m* = 3 at β = 1.1, coinciding with the onset of a symmetry-breaking (SB) phenomenon characteristic of the β model, in which additional modes with even wave numbers (k = 2, 4) become excited. Notably, this SB transition is not detected by the linear PCA-based approach.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 9","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148944452","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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