{"title":"Adaptive multi-scale hierarchical method for complex network key nodes identification.","authors":"Xiaoyang Liu, Wanqian Zhang, Asgarali Bouyer, Na Zhao, Xiaofang Xia, Hocine Cherifi","doi":"10.1063/5.0348978","DOIUrl":"https://doi.org/10.1063/5.0348978","url":null,"abstract":"<p><p>Traditional centrality measures normally rely on a single topological scale, which limits their ability to comprehensively characterize the roles of nodes across local, semi-local, and global network structures. Moreover, their generalization capability across different network types is often weak, leading to low accuracy in identifying key nodes. To solve these limitations, this paper has proposed an adaptive multi-scale hierarchical method for key nodes identification in complex networks, called AdaMH. First, a hierarchical structural influence framework is constructed by integrating local, semi-local, and global topological scales. Second, an adaptive entropy weight allocation strategy based on information entropy is employed to achieve robust fusion of multi-scale structural features. Finally, extensive comparative analysis experiments are conducted on nine real-world datasets against five well-known baseline methods. Experimental results under the SIR spreading model prove that the top-10 nodes identified by AdaMH increase the final infection range by 1% to 156% compared with baseline methods. These results indicate that AdaMH effectively captures synergistic relations among multi-scale structural features, thereby providing an efficient identification of key nodes. In addition, the proposed method can also be applied in the field of fraudulent node mining.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 10","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149126783","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}
{"title":"Solitons and their clusters sustained in saturable cubic-quintic nonlinear lattices.","authors":"Jiawei Li, Yufan Xie, Milivoj R Belić, Jincheng Shi, Xing Zhu, Liangwei Zeng","doi":"10.1063/5.0351143","DOIUrl":"https://doi.org/10.1063/5.0351143","url":null,"abstract":"<p><p>We systematically investigate one- and two-dimensional (1D and 2D) solitons in periodically modulated media with saturable cubic and quintic nonlinearities, governed by a modified nonlinear Schrödinger equation. We discuss two distinct nonlinear regimes: purely focusing cubic-quintic media and inverted cubic-quintic media-featuring defocusing cubic and focusing quintic terms. Using the modified squared-operator method and Fourier collocation method, we analyze the existence domains, waveforms, powers and propagation constant relationships, and linear stability of fundamental solitons and their clusters. Our findings demonstrate that the combined action of saturable nonlinearities and nonlinear lattices effectively suppresses critical collapse and stabilizes diverse soliton structures, without relying on external linear periodic potentials or Bloch energy band theory. In both 1D and 2D systems, single solitons and their clusters tend to stabilize at larger propagation constants, with clusters exhibiting superior stability. Furthermore, the saturation coefficients S1 and S2 regulate the existence ranges, imposing strong saturation constraints on the propagation constants. In the competing (inverted) cubic-quintic nonlinearities, stable solutions exist only when S2 > S1. These results enrich the understanding of stable nonlinear localized modes in composite media with saturable nonlinearities and offer a theoretical framework for controlling optical localized modes in complex media, with potential applications in all-optical communication and information processing.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 10","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149191641","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}
Xu Wang, James Macinko, Maurizio Porfiri, Rifat Sipahi
{"title":"On the role of economic hardship in gun acquisition in the United States.","authors":"Xu Wang, James Macinko, Maurizio Porfiri, Rifat Sipahi","doi":"10.1063/5.0346479","DOIUrl":"https://doi.org/10.1063/5.0346479","url":null,"abstract":"<p><p>Gun-related violence in the U.S. threatens public health and strains the healthcare system. Prior work suggests that self-protection is a key driver of gun prevalence in the U.S., whereby Americans seek to acquire a gun when they fear that they themselves or their loved ones may be at risk of violence. The more the gun homicides take place in a city, the stronger the tendency to own a gun by its residents. While it is tenable that economic conditions may modulate the strength of this association, we know little about how economic hardship shapes gun ownership in the U.S. Leveraging mutual information and time-series symbolization, and considering suicides with firearms as a proxy of gun prevalence, we examine how economic indicators modify the association between gun homicides and gun prevalence using a cross-sectional comparison of 884 metropolitan/micropolitan statistical areas in the U.S. and a temporal analysis of national monthly trends. Across these areas, gun prevalence rises roughly twice as fast with gun homicides in high income-inequality settings. Nationally, gun homicide-gun prevalence association emerges only when Economic Policy Uncertainty changes are sufficiently large. These findings suggest that reducing inequality and elevating economic confidence past a critical threshold may dampen gun prevalence and help mitigate public-health impacts of gun violence.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 10","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149104610","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}
{"title":"D-Lax-Pair-FIND: Data-driven reconstruction of the evolution operators in Lax pairs for discrete integrable equations.","authors":"Shuning Lin, Yong Chen","doi":"10.1063/5.0336825","DOIUrl":"https://doi.org/10.1063/5.0336825","url":null,"abstract":"<p><p>The Lax pair stands as a central concept in the theory of integrable systems, whose discovery holds considerable significance for solving and analyzing nonlinear evolution equations. To address the challenge of discovering Lax pairs from observational data, we propose D-Lax-Pair-FIND, a data-driven methodology that synergistically combines deep learning with sparse regression to automatically discover the evolution operators in Lax pairs of discrete integrable equations with known spectral operators. The approach employs fully connected feedforward neural networks to approximate solutions of semi-discrete systems, treating the discrete spatial variable as continuous to enable interpolation at non-integer lattice points. By constructing a predefined library of candidate operators and leveraging sparse regularization techniques, the method automatically identifies the linear evolution operators. The loss function comprises three key components: data-fitting loss, discrete Lax compatibility loss, and sparse regularization loss. Through joint optimization of the neural network parameters and the sparse coefficient vector, the method achieves robust discovery of Lax pairs. Numerical experiments demonstrate that the proposed framework successfully recovers the evolution operators in Lax pairs for several classical discrete integrable systems, including the self-dual network equation, the Ablowitz-Ladik equation, and the Toda lattice-covering both the form with explicit spectral parameters and the operator form. This research provides an effective and general computational framework for automatically uncovering the intrinsic structure of discrete integrable systems from limited data, with potential implications for advancing data-driven studies in integrable systems theory.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 10","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149104852","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}
{"title":"A novel route for saving cooperation on dynamical networks: Enhancing rationality.","authors":"Yuanxin Liu, Bin Wu","doi":"10.1063/5.0354201","DOIUrl":"https://doi.org/10.1063/5.0354201","url":null,"abstract":"<p><p>Cooperation is crucial for all levels of living systems. The last two decades have seen progress in revealing the mechanisms for cooperation in structured populations. Most of those analytical works have an explicit assumption, i.e., weak rationality or high temperature in statistical physical terms. It is still far from known how rationality alters the fate of cooperation, although simulation results have provided some intuitions. To be specific, the analytical insight is still lacking under what conditions cooperation can still be promoted, given that it cannot be favored by weak rationality. To this end, we investigate a coevolutionary model where both strategy and network evolve simultaneously. We give a sufficient condition under which cooperation cannot be favored for weak-selection limit, but it can be rescued by enhancing rationality alone. Furthermore, we give the critical rationality analytically. Counterintuitively, we show that the critical rationality can be larger if cooperator-defector links are more fragile, indicating that robust cooperator-defector social relationships can rescue cooperation. We, thus, show that increasing rationality intensity alone can rescue cooperation, where it cannot be present under weak-selection limit. Our work calls for an extrapolation from weak rationality in evolutionary game theory.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 10","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149104911","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}
{"title":"Cardiac repolarization wave dynamics and its role in arrhythmogenesis.","authors":"Hung-Yi Ly, Alain Karma","doi":"10.1063/5.0345361","DOIUrl":"https://doi.org/10.1063/5.0345361","url":null,"abstract":"<p><p>Premature ventricular contractions (PVCs) are commonly associated with action potential duration (APD) prolongation through early afterdepolarizations (EADs) or repolarization failure (RF), yet the mechanisms linking spatial heterogeneity of repolarization to PVC initiation remain unclear. Previous studies have emphasized the role of repolarization gradients, but a unifying dynamical framework connecting repolarization wave (RW) propagation and PVC initiation is lacking. Here, we investigate PVC initiation in one-dimensional heterogeneous tissue using models of increasing biophysical complexity ranging from simplified two-variable to detailed ionic models. Across all models, we find that PVC initiation is governed by a dynamical competition at the interface between long- and short-APD regions. A PVC occurs when the short-APD region regains excitability before a retrograde RW succeeds to propagate into the long-APD region. The retrograde RW speed, therefore, provides a quantitative indicator of this competition and is determined by the stability of the high-voltage plateau fixed point associated with EADs or RF. Depending on this stability, retrograde RWs propagate as trigger waves when the fixed point is stable or as pushed or pulled fronts when unstable. A highly stable fixed point slows the RW, thereby promoting PVC initiation by allowing more time for the recovery of the short-APD region. For the two-variable models, we derive semi-analytical criteria predicting the conditions for PVC initiation. Finally, we show that the critical size of the prolonged APD region is comparable to the electrotonic coupling length under diffusive coupling and is significantly reduced by ephaptic coupling, which facilitates PVC initiation and arrhythmogenesis.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 10","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149179679","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}
{"title":"Graph diffusion convolution on multivariate weighted joint recurrence networks for seizure-state classification in intracranial EEG.","authors":"Qing Cai, Yushi Hao, Jianpeng An, Chao Ma, Mengyu Li, Zhongke Gao","doi":"10.1063/5.0344726","DOIUrl":"https://doi.org/10.1063/5.0344726","url":null,"abstract":"<p><p>Discriminating interictal and ictal brain states is important for both seizure-state classification and the characterization of seizure-related network reorganization in drug-resistant epilepsy. Intracranial electroencephalography (iEEG) provides high-resolution recordings of brain activity, but its sparse, irregular, and patient-specific electrode geometry requires models that go beyond Euclidean representations. In this work, we propose a multivariate weighted joint recurrence network coupled with a graph diffusion convolution network for binary interictal/ictal classification. Each iEEG segment is first embedded into a reconstructed phase space and transformed into a recurrence-based functional network, in which weighted edges quantify nonlinear dynamical coupling between implanted contacts. A graph diffusion convolution mechanism is then applied to capture higher-order dependencies across the implanted brain topology. On a nine-patient subset of the Hospital of the University of Pennsylvania iEEG Epilepsy Dataset, the proposed framework achieved an average accuracy of 93.4% and outperformed standard graph convolutional and Euclidean deep-learning baselines. In addition, recurrence networks derived from ictal and interictal periods showed state-dependent differences in weighted topological organization, suggesting seizure-related reconfiguration of nonlinear brain-network dynamics. These results indicate that recurrence-based graph diffusion provides an effective and interpretable nonlinear framework for seizure-state classification and for modeling ictal network reorganization in iEEG.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 10","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149104599","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}
Vinoth Seralan, Sabarathinam Srinivasan, Anitha Karthikeyan, Karthikeyan Rajagopal, Viktor Popov
{"title":"Spatiotemporal dynamics in the bi-layer memristive Morris-Lecar neurons with different obstacles.","authors":"Vinoth Seralan, Sabarathinam Srinivasan, Anitha Karthikeyan, Karthikeyan Rajagopal, Viktor Popov","doi":"10.1063/5.0340752","DOIUrl":"https://doi.org/10.1063/5.0340752","url":null,"abstract":"<p><p>We report spiral-wave transitions in the memristive Morris-Lecar neuron model with differently structured obstacles in single and bilayer configurations. Wave propagation is initiated by applying an external periodic stimulus to the left-side nodes of the excitable media. During interactions with obstacles, rich spiral patterns emerge in both single-layer and bilayer configurations across various amplitudes and frequencies of the external stimulus, as well as for different diffusion coefficients. The spatio-energy is also calculated to demonstrate the existence of a spiral core within stable spiral waves. The statistical synchronization factor is computed over a range of diffusion coefficients to assess the presence of spiral waves and the absence of instabilities. Building on these single-layer dynamics, we then investigate multilayer effects by extending our study to a bilayer system, with one layer containing obstacles. We observe the transition of spiral waves between the layers across these various stimulus parameters, as well as for different intralayer coupling coefficients. Finally, the trend of synchronization between the two layers is investigated using the spatial interlayer synchronization error across a range of interlayer coupling strengths. The important findings of the present study are discussed in the conclusion.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 10","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149104600","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}
Matvei M Khamkov, Maxim I Bolotov, Lev A Smirnov, Igor Belykh
{"title":"Birth and breakdown of breathing and rotobreathing cyclops states in Kuramoto networks with higher-mode coupling.","authors":"Matvei M Khamkov, Maxim I Bolotov, Lev A Smirnov, Igor Belykh","doi":"10.1063/5.0353880","DOIUrl":"https://doi.org/10.1063/5.0353880","url":null,"abstract":"<p><p>Cluster synchronization states often serve as organizing centers for collective dynamics, but their destabilization can open unexpected routes to both coherent and incoherent behaviors. We study such transitions for cyclops states in globally coupled networks of identical Kuramoto-Sakaguchi rotators with inertia and two-harmonic coupling. Stationary cyclops states consist of two coherent clusters and a solitary oscillator that maintains fixed phase differences with the clusters. Using Floquet analysis and numerical continuation of periodic orbits, we trace bifurcation routes for the birth and breakdown of breathing and rotobreathing cyclops states with nonstationary intercluster phase differences. Breathing cyclops states, born from their stationary counterparts, correspond to bounded oscillations of the intercluster phases. They lose stability via period-doubling bifurcations, which produce phase-split cyclops states whose intercluster motion repeats only after two cycles of the parent breather, or via cluster-destruction bifurcations. Rotobreathing cyclops states, in which the intercluster phase differences undergo full rotations, are not, in general, merely breathing cyclops states whose oscillation amplitude has grown sufficiently large; rather, they predominantly arise through global bifurcations involving heteroclinic-contour-like structures formed by saddle cluster states. We further show that these states have wide basins of attraction, persist in large odd-sized networks, and contrast sharply with even-sized networks, where stationary multi-cluster states dominate. These results identify higher-mode coupling and solitary-oscillator-mediated rotations as generic mechanisms for organizing complex cluster motion in phase oscillator networks.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 10","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149104829","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}
Christopher D Marcotte, Matthew J Hoffman, Flavio H Fenton, Elizabeth M Cherry
{"title":"Strongly and weakly coupled data assimilation for reconstruction of three-dimensional synthetic and experimental cardiac electrical excitation states with sparse observations.","authors":"Christopher D Marcotte, Matthew J Hoffman, Flavio H Fenton, Elizabeth M Cherry","doi":"10.1063/5.0335582","DOIUrl":"https://doi.org/10.1063/5.0335582","url":null,"abstract":"<p><p>Data assimilation practitioners must make design decisions regarding the influence of uncertainties across space, time, and interdependent channels. Using the local ensemble transform Kalman filter, we investigate how different information sharing strategies, namely, strong and weak coupling, affect our ability to reconstruct electrical activity in the heart from sparse observations of state. These two coupling approaches differ in whether observations of one variable are allowed to influence others during the update step. We analyze the potential of a single observation to affect the ensemble weights and span through the spectral properties of the analysis operators. We apply weak and strong coupling in assimilations of observations generated from a numerical model of scroll-wave turbulence and find that restricting information flow from the observations across variable fields (weak coupling) in the low-model error case is effective at improving reconstruction accuracy and robustness. Weak coupling is relatively detrimental for high-model-error reconstructions, and strong coupling produces more reliable estimates of the state. We also consider a case where observations are derived from paced cardiac tissue where only surface voltage is recorded and find in that scenario that while both coupling methods achieve similar degrees of accuracy, strong coupling more closely approximates fine details in the observations, whereas weak coupling provides greater robustness. We conclude that coupling has marginal influence on reconstruction accuracy for cardiac electrical excitation except in extreme cases, i.e., where high-model error precludes accurate reconstruction.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 10","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149179711","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}