Chaos最新文献

{"title":"Unveiling periodic structures, period-bubbling, and multistability in a fractional-order system with Allee effect.","authors":"Prajjwal Gupta, Anupam Priyadarshi","doi":"10.1063/5.0323801","DOIUrl":"https://doi.org/10.1063/5.0323801","url":null,"abstract":"<p><p>Nonlinear ecological systems exhibit rich dynamical behaviors, such as organized periodic structures, sudden transitions between attractors, period-bubbling, and multistability. While these features are well-documented in integer-order and discrete-time ecological models, their persistence under memory-driven dynamics remains largely unexplored. In this study, we investigate these nonlinear phenomena in a tri-trophic fractional-order ecological system incorporating an Allee effect. Analytically, the well-posedness of the system is established, and the existence of equilibria, along with the conditions for the local and global stability, is explored. The existence criteria for Hopf bifurcations are also discussed with respect to the fractional-order and the Allee parameter. To characterize the global dynamics, we have constructed two-parameter largest Lyapunov exponent plots for a fractional-order ecological system, together with high-resolution isospike diagrams. These diagrams reveal that the fractional-order system preserves the classical organized periodic windows, such as shrimp-shaped structures, double fish-hook patterns, and periodic strips. The system also shows a transition from periodicity to chaos through Feigenbaum-type scaling of periods. Most importantly, our results show that the fractional-order ecological system exhibits period-bubbling and multistability, two hallmark features of nonlinear dynamics that have been rarely explored in memory-driven ecological systems. Thus, although memory smoothens the transitions between attractors, the introduction of memory into the ecological systems does not eliminate the core features of nonlinearity known from integer-order and discrete-time systems.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 5","pages":""},"PeriodicalIF":3.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147811669","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 general framework for neural delay differential equations with various delay types.","authors":"Jiaxuan Zhang, Qunxi Zhu, Wei Lin","doi":"10.1063/5.0325998","DOIUrl":"https://doi.org/10.1063/5.0325998","url":null,"abstract":"<p><p>This work proposes a general framework for Neural Delay Differential Equations (NDDEs), a class of continuous-depth neural networks, namely, the Generalized NDDEs (GNDDEs), incorporating various types of delays beyond the previously considered constant delays, including time-dependent, state-dependent, and time-state-dependent delays. Furthermore, we employ a simulation-free training strategy for the vector field, allowing the system reconstruction directly from the irregularly sampled time series without the prior model knowledge. Specifically, we perform the regression between the preprocessed target and parameterized vector fields, bypassing the need to numerically solve the differential equations as required in conventional time-series regression. Additionally, GNDDEs enable adaptive, model-free identification of the delay functions, along with the model-based identification of the system parameters. The experimental results demonstrate that the proposed framework exhibits the notable effectiveness and computational efficiency across a variety of delay differential equation problems, further broadening the applicability of continuous-depth neural networks in the delay system modeling.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 5","pages":""},"PeriodicalIF":3.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147811696","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":"Frequency synchronization facilitated by frequency differences: Dynamics of coupled-oscillator systems with damaged elements.","authors":"Shota Inagawa, Hiroki Hata, Shigefumi Hata","doi":"10.1063/5.0305666","DOIUrl":"https://doi.org/10.1063/5.0305666","url":null,"abstract":"<p><p>This study investigates the synchronization dynamics of coupled-oscillator systems in which some of the oscillators are damaged and lose their autonomous oscillations. The damaged elements are modeled using damped oscillators; thus, the system is composed of both limit-cycle oscillators and damped oscillators. In this system, as is commonly observed in conventional coupled limit-cycle oscillators, frequency synchronization among oscillators is destroyed when the difference between the natural frequencies of the oscillators increases. However, in the presence of damped oscillators, frequency synchronization can be facilitated by further increasing the frequency difference from the desynchronization state. We conduct numerical simulations on coupled Stuart-Landau oscillators and investigate this reentrance of frequency synchronization systematically. We also propose an approximate theory to predict the stability of the synchronization state based on a linear stability analysis of the fixed point, which reveals the appearance of the Hopf modes. Using this theory, we argue that the reentrance of frequency synchronization driven by increasing frequency differences can be observed in a wide range of coupled-oscillator systems with damaged elements.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 5","pages":""},"PeriodicalIF":3.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147833727","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":"An adaptive resource allocation mechanism based on patch cluster structures: Coupling resource flow and epidemic spreading dynamics in metapopulation networks.","authors":"Nan Chen, Liang'an Huo, Yue Yu","doi":"10.1063/5.0317618","DOIUrl":"https://doi.org/10.1063/5.0317618","url":null,"abstract":"<p><p>Epidemic outbreaks threaten global health and stability, creating an urgent need for effective resource allocation strategies. Existing studies often neglect dynamic regional risk adjustments and resource coordination based on cluster structures. To address this, this paper proposes an adaptive resource allocation mechanism based on the patch cluster structures and develops a coupled dynamics model that integrates resource flow with epidemic spreading in a metapopulation network. The model employs a migration-interaction-return process to characterize both inter-patch migration and intra-patch epidemic spreading. Furthermore, an adaptive resource allocation mechanism is designed, which dynamically adjusts both inter-patch donation strategies and intra-cluster allocation schemes according to evolving, patch-specific risk levels, thereby realizing dynamic optimization of resource distribution. Using the micro Markov chain approach, we derive epidemic evolution equations and calculate infection thresholds. Numerical simulations validate the model and examine key parameter impacts. The results show that increasing patch cluster numbers, enhancing inter-cluster connectivity, and improving cluster efficiency-especially in networks with abundant triangular structures-effectively raise the epidemic threshold and reduce infection scale. Compared to traditional models, adaptive resource allocation models can utilize resources more efficiently, thereby decreasing the infection scale. Higher donation/utilization rates mitigate global spread, while targeted assistance from high-risk to low-risk patches lowers overall prevalence. This study provides a theoretical framework for dynamic group resource optimization in heterogeneous risk environments, offering valuable insights for epidemic prevention and control.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 5","pages":""},"PeriodicalIF":3.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147811614","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":"Modeling the influence of interactions on different variables in a turbulent thermoacoustic system.","authors":"Aneesh Srivatsa, Shruti Tandon, Andrea Elizabeth Biju, Norbert Marwan, Jürgen Kurths, R I Sujith","doi":"10.1063/5.0313251","DOIUrl":"https://doi.org/10.1063/5.0313251","url":null,"abstract":"<p><p>Turbulent reacting flows confined to ducts are plagued by thermoacoustic instability, a state in which a positive feedback between flow, flame, and acoustic perturbations leads to the emergence of catastrophically high-amplitude oscillatory dynamics in the sound and global heat release rate fluctuations. Modeling the interdependence between local interactions and the global emergence of order in such spatially extended complex systems is exacting. Here, we present a novel reduced-order model to capture the influence of the local interactions on distinct variables exhibiting global emergence of order in a turbulent reacting flow system. We represent each variable that exhibits global oscillatory instability as an oscillator with a cubic nonlinearity. The oscillator is driven by a forcing term that represents the holistic influence of the inter-subsystem interactions on the global behavior. The forcing term essentially couples the local interactions and the globally emergent dynamics in the model. Further, the influence of the inter-subsystem interactions on the behavior of each subsystem is different. Therefore, we use different forcing terms for each variable inspired by the physical interactions in the system. The nonlinear oscillators representing the acoustic and the heat release rate oscillations are hence forced using Wiener and Markov-modulated Poisson processes, respectively. Using this approach, we are able to reproduce (i) the multifractal characteristics of acoustic pressure fluctuations during chaotic dynamics, (ii) the loss of multifractality through the experimentally observed scaling law behavior during the transition from chaos to order, and (iii) the emergence of periodicity and bifurcation in heat release rate dynamics.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 5","pages":""},"PeriodicalIF":3.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147833754","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":"Robust fault classification in rotary machines using recurrence quantification analysis features for machine learning techniques.","authors":"Ayham Zaitouny, Anusuya Krishnan, Houssam Abdul-Rahman, Yaman Sabsabi, Yousef Salah, Osama Al Mukbel, Rafat Damseh, Nazar Zaki","doi":"10.1063/5.0320309","DOIUrl":"https://doi.org/10.1063/5.0320309","url":null,"abstract":"<p><p>Fault detection in rotatory machines is an important necessity to provide system operational reliability and lower unexpected downtime in industrial systems. Conventional feature extraction methods, although good in controlled situations, tend to fall short in noisy situations that mirror real-world operation situations. To fulfill this gap, this work explores machine learning classifiers-Random Forest (RF), Gradient Boosting (GB), XGBoost (XGB), and LightGBM (LGBM)-with two different feature sets: statistical features and Recurrence Quantification Analysis (RQA) features. First, we systematically validate the proposed framework by benchmarking recurrence-based dynamical features against conventional statistical features on a synthetic nonlinear benchmark composed of four well-established dynamical systems: the Lorenz system, the Rössler system, the Hénon map, and the Duffing oscillator. This controlled evaluation enables a methodological comparison across distinct nonlinear regimes before applying the framework to industrial fault data. Then, using experimental rotary machines data, we further examine the robustness of the classifiers under two different operation situations: noise-free and noise-included situations. In a noise-free situation, all classifiers resulted near perfect classification with all statistical features obtaining 99%, whereas RQA features resulted similarly around 93%. Yet, when a Gaussian noise is added (15%-75% of signal magnitude), statistical features marked a considerable decline to 85% accuracy, whereas RQA features remained highly efficient above 94%; consistent results were obtained when other types of noise were added, namely, Brownian noise and impulsive noise. These results present a demonstration of RQA-based feature superiority in long-term dynamics capture and cite its potential to provide a more reliable fault detection in industrial practice where the use of noise and variability of environments is an inescapable consequence.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 4","pages":""},"PeriodicalIF":3.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147627233","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":"Basin of attraction analysis in generalized swing equation via dynamical renormalization group approach.","authors":"Xinyu Zhou, Zejing Zhang, Miao Han, Zixiang Yan, Jian Gao, Meng Zhan, Yueheng Lan, Jinghua Xiao","doi":"10.1063/5.0314344","DOIUrl":"https://doi.org/10.1063/5.0314344","url":null,"abstract":"<p><p>As renewable energy integration continues to accelerate, transient stability challenges in modern power systems have become increasingly pronounced, particularly due to the systems' inherent high-dimensional nonlinear dynamics. Developing a reliable and efficient method for assessing transient stability and the associated basin of attraction remains a critical yet unresolved challenge. This study focuses on the precise estimation of the basin-of-attraction boundary in phase-locked loop based voltage source converter systems, which can be described by a generalized swing equation. To address this problem, a higher-order Taylor expansion renormalization approach is proposed. This method enables the construction of a highly accurate approximation of the stable manifold that serves as the basin-of-attraction boundary, offering substantial improvements over conventional linear and second-order local approximations. The reliability and effectiveness of the proposed approach are rigorously validated through simulations under various fault scenarios in the transient stability assessment. The proposed method provides a robust tool for analyzing transient stability in modern power systems and offers new insights into the stability characterization of other nonlinear dynamical systems.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 4","pages":""},"PeriodicalIF":3.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147728564","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":"Noise-induced transients in the propagation of epidemic with higher-order interactions.","authors":"Rong Yuan, Zhen Jin, Maoxing Liu","doi":"10.1063/5.0302152","DOIUrl":"https://doi.org/10.1063/5.0302152","url":null,"abstract":"<p><p>During epidemic propagation governed by a susceptible-infected-susceptible process, infectious disease dynamics exhibit transients between stable equilibrium states. This study identifies noise as a key factor in inducing such transients, leading to an earlier onset of tipping points in both outbreak and recovery phases. A network epidemic model incorporating higher-order interactions is formulated, along with its reduced form. The impact of noise is examined separately for models with and without higher-order interactions. The results show that environmental noise advances epidemic outbreaks by lowering the tipping threshold, whereas demographic noise facilitates faster recovery transitions. Moreover, higher-order interactions amplify nonlinear feedbacks, widening the hysteresis between the outbreak and the recovery and prolonging transient durations. A theoretical framework is then established to describe the dependence of the mean transient time on noise intensity, highlighting the role of noise-induced transients in shaping epidemic thresholds and control strategies.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 4","pages":""},"PeriodicalIF":3.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147590116","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":"Nonparametric testing of spatial dependence in 2D and 3D random fields.","authors":"Christian H Weiß, Philipp Adämmer","doi":"10.1063/5.0307955","DOIUrl":"https://doi.org/10.1063/5.0307955","url":null,"abstract":"<p><p>We propose a flexible and robust nonparametric framework for testing spatial dependence in two- and three-dimensional random fields. Our approach involves converting spatial data into one-dimensional time series using space-filling Hilbert curves. We then apply ordinal pattern-based tests for serial dependence to this series. Because Hilbert curves preserve spatial locality, spatial dependence in the original field manifests as serial dependence in the transformed sequence. The approach is easy to implement, accommodates arbitrary grid sizes through generalized Hilbert (\"gilbert\") curves, and naturally extends beyond three dimensions. This provides a practical and general alternative to existing methods based on spatial ordinal patterns, which are typically limited to two-dimensional settings.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 4","pages":""},"PeriodicalIF":3.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147644244","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":"Melnikov-Arnold integrals and optimal normal forms.","authors":"Ivan I Shevchenko","doi":"10.1063/5.0307886","DOIUrl":"https://doi.org/10.1063/5.0307886","url":null,"abstract":"<p><p>The Melnikov-Arnold integrals (MA-integrals) is a well-known instrument used to measure the splitting of separatrices in Hamiltonian systems. In this article, we explore how calculation of MA-integrals can be used as well to estimate sizes of secondary resonances. Within the standard map model, we show how the newly developed MA-based procedure allows one to estimate the sizes of secondary resonances of any order (up to the order of the optimal normal form), without relying on the cumbersome traditional normalization procedure.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 4","pages":""},"PeriodicalIF":3.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147670816","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}