IF 2.7 2区数学

Chaos Pub Date : 2025-05-01 DOI: 10.1063/5.0241166

Dan Crisan, Michael Ghil, Rohan Nuckchady

{"title":"Exponential stability for a forecast-assimilation process with unstable dynamics.","authors":"Dan Crisan, Michael Ghil, Rohan Nuckchady","doi":"10.1063/5.0241166","DOIUrl":"https://doi.org/10.1063/5.0241166","url":null,"abstract":"Data assimilation, a vital process in areas such as numerical weather prediction, integrates observational data into computational models to provide accurate forecasts. In this study, we conceptualize the forecast-assimilation (FA) process as a dynamic-stochastic system driven by time-dependent observational data. The core objective is to investigate the stability of this process with respect to variations in its initial conditions, particularly when the underlying system dynamics, referred to here as the signal, exhibit instability. We provide a rigorous analysis for both linear and nonlinear dynamics to determine conditions under which the FA process remains stable. In the nonlinear case, we identify an exponential semi-group whose stability is used to prove a uniform in time bound on the expected Wasserstein distance between the true FA process and one that is incorrectly initialized. For linear dynamics, we prove that the FA process converges both weakly and in the Wasserstein topology to a \"nominal\" one. For this, we use a representation of the FA process by means of the classical Kallianpur-Striebel formula. We show that the Wasserstein distance between the FA process correctly initialized and one which is incorrectly initialized converges to 0 exponentially fast provided the wrong initial condition is absolutely continuous with respect to the correct initial condition.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143974704","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

Biodiversity-induced opposing shifts of tipping points in mutualistic ecological networks. 生物多样性引发了共生生态网络中临界点的对立转移。

IF 2.7 2区数学

Chaos Pub Date : 2025-05-01 DOI: 10.1063/5.0260836

Fei Xu, Meng Jin, Chuansheng Shen, Hong Qi, Shoufang Huang, Maosheng Wang, Jiqian Zhang, Xiang Li

{"title":"Biodiversity-induced opposing shifts of tipping points in mutualistic ecological networks.","authors":"Fei Xu, Meng Jin, Chuansheng Shen, Hong Qi, Shoufang Huang, Maosheng Wang, Jiqian Zhang, Xiang Li","doi":"10.1063/5.0260836","DOIUrl":"https://doi.org/10.1063/5.0260836","url":null,"abstract":"While biodiversity is recognized as crucial for ecosystem stability, the mechanisms governing its dual role in collapse and restoration dynamics remain unclear. By analyzing ten empirical plant-pollinator mutualistic networks, we uncover a biodiversity paradox: increased biodiversity lowers the collapse threshold while enhancing restoration potential. This counterintuitive phenomenon is quantitatively linked to a significant negative correlation between biodiversity levels and hysteresis loop width. To understand this paradox, we develop a refined degree-weighted mean-field framework, reducing high-dimensional dynamics to a tractable two-dimensional system. By integrating potential landscape theory from nonequilibrium statistical mechanics, we uncover the physical basis of biodiversity-driven threshold shifts. Systematic modulation of mutualistic interaction degrees across stochastic networks further confirms the universal regulatory role of reduced biodiversity in collapse-restoration tipping points. Our findings provide a quantitative framework for predicting ecosystem resilience and optimizing restoration strategies across biodiversity gradients.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144062562","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

Data driven discovery of escape phenomena in stochastic systems. 随机系统中逃逸现象的数据驱动发现。

IF 2.7 2区数学

Chaos Pub Date : 2025-05-01 DOI: 10.1063/5.0264403

Jiangyan Liu, Jiaqian Zhao, Ming Yi, Jinqiao Duan, Xiaoli Chen

{"title":"Data driven discovery of escape phenomena in stochastic systems.","authors":"Jiangyan Liu, Jiaqian Zhao, Ming Yi, Jinqiao Duan, Xiaoli Chen","doi":"10.1063/5.0264403","DOIUrl":"https://doi.org/10.1063/5.0264403","url":null,"abstract":"Stochastic dynamical systems, influenced by random disturbances, exhibit complex behaviors that are critical to understanding in various fields, such as physics, biology, and finance. The study of escape phenomena, where systems transition from stable states under the influence of noise, is essential for analyzing the dynamical behavior and learning the stochastic dynamics. This paper focuses on two key deterministic quantities, the mean exit time and the escape probability, which are widely used to analyze escape characteristics in stochastic dynamical systems. Traditional methods for computing escape problems, such as the finite difference method, finite element method, finite volume method, and Monte Carlo simulations, face challenges in high-dimensional systems and irregular domains. To address these limitations, we propose a comprehensive framework based on physics-informed neural networks. This framework is designed to solve both forward and inverse problems of escape phenomena in stochastic systems driven by Brownian motion. Our approach eliminates the need for mesh generation and naturally accommodates irregular domains, achieving a better balance between computational efficiency and accuracy. It not only overcomes the drawbacks of traditional numerical methods in solving mean exit time and escape probability but also enables learning stochastic dynamics from escape data. Through a series of numerical examples, we demonstrate the effectiveness and accuracy of the proposed method.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144109975","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

Intermittent spike train processing through fractional leaky integrate-and-fire neuromorphic unit. 断断续续的尖峰序列处理通过分数泄漏整合-火神经形态单元。

IF 2.7 2区数学

Chaos Pub Date : 2025-05-01 DOI: 10.1063/5.0251233

R T Sibatov, A K Gavrilova, A I Savitskiy, Yu P Shaman, A V Sysa

引用次数: 0

Tipping in an adaptive climate network model. 自适应气候网络模型中的倾斜度。

IF 2.7 2区数学

Chaos Pub Date : 2025-05-01 DOI: 10.1063/5.0256156

T Bdolach, J Kurths, S Yanchuk

{"title":"Tipping in an adaptive climate network model.","authors":"T Bdolach, J Kurths, S Yanchuk","doi":"10.1063/5.0256156","DOIUrl":"https://doi.org/10.1063/5.0256156","url":null,"abstract":"With rising global temperatures, Earth's tipping elements are becoming increasingly more vulnerable to crossing their critical thresholds. The reaching of such tipping points does not only impact other tipping elements through their connections but can also have further effect on the global mean surface temperature (GMT) itself, either increasing or decreasing the probability of further tipping points being reached. Recently, a numerical study analyzing the risk of tipping cascades has been conducted, using a conceptual model describing the dynamics of a tipping element with its interactions with other tipping elements taken into account [N. Wunderling, J. F. Donges, J. Kurths, and R. Winkelmann, Earth Syst. Dyn. 12, 601-619 (2021)]. Here, we extend the model substantially by including adaptation so that the GMT feedback induced by the crossing of a tipping point is incorporated as well. We find that although the adaptive mechanism does not impact the risk for the occurrence of tipping events, large tipping cascades are less probable due to the negative GMT feedback of the ocean circulation systems. Furthermore, several tipping elements can play a different role in cascades in the adaptive model. In particular, the Amazon rainforest could be a trigger in a tipping cascade. Overall, the adaptation mechanism tends to slightly stabilize the network.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144149555","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

Exploring localization in nonlinear oscillator systems through network-based predictions. 通过基于网络的预测探索非线性振荡器系统的局部化。

IF 2.7 2区数学

Chaos Pub Date : 2025-05-01 DOI: 10.1063/5.0265366

Charlotte Geier, Norbert Hoffmann

{"title":"Exploring localization in nonlinear oscillator systems through network-based predictions.","authors":"Charlotte Geier, Norbert Hoffmann","doi":"10.1063/5.0265366","DOIUrl":"https://doi.org/10.1063/5.0265366","url":null,"abstract":"Localized vibrations, arising from nonlinearities or symmetry breaking, pose a challenge in engineering, as the resulting high-amplitude vibrations may result in component failure due to fatigue. During operation, the emergence of localization is difficult to predict, partly because of changing parameters over the life cycle of a system. This work proposes a novel, network-based approach to detect an imminent localized vibration. Synthetic measurement data are used to generate a functional network, which captures the dynamic interplay of the machine parts, complementary to their geometric coupling. Analysis of these functional networks reveals an impending localized vibration and its location. The method is demonstrated using a model system for a bladed disk, a ring composed of coupled nonlinear Duffing oscillators. Results indicate that the proposed method is robust against small parameter uncertainties, added measurement noise, and the length of the measurement data samples. The source code for this work is available at C. Geier [(2024). \"Code for paper Exploring localization in nonlinear oscillator systems through network-based predictions,\" Zenodo. https://doi.org/10.5281/zenodo.12611988].","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143975279","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 of commuter rioters and income distribution on the 2019 Chilean unrest. 通勤暴徒和收入分配对2019年智利骚乱的影响。

IF 2.7 2区数学

Chaos Pub Date : 2025-05-01 DOI: 10.1063/5.0256672

Carlos Cartes

引用次数: 0

Impact of combined effects of vectors, protective measures, and vaccination under threshold policy control on the SISV model. 阈值政策控制下媒介、保护措施和疫苗接种的联合效应对SISV模型的影响。

IF 2.7 2区数学

Chaos Pub Date : 2025-05-01 DOI: 10.1063/5.0256966

Xiong Zhang, Zhongyi Xiang

{"title":"Impact of combined effects of vectors, protective measures, and vaccination under threshold policy control on the SISV model.","authors":"Xiong Zhang, Zhongyi Xiang","doi":"10.1063/5.0256966","DOIUrl":"https://doi.org/10.1063/5.0256966","url":null,"abstract":"This paper introduces a novel class of Filippov susceptible-infected-susceptible-vaccinated model that considers the combined effects of media coverage, protective measures, and vaccination. Unlike traditional models that focus on a single control measure, this study reveals more intricate dynamic behaviors arising from the synergistic impact of these three strategies. We use the scale of infected individuals and their rate of change as criteria for implementing control measures, conducting a comprehensive evaluation. By utilizing the characteristics of the Lambert W function, we effectively convert these criteria into a threshold value linked to the susceptible population, thereby facilitating the analysis of the dynamic behaviors of the two subsystems. Utilizing the theoretical framework of Filippov systems, we derive the conditions for the existence of sliding segments, sliding dynamics, various types of equilibria, and the occurrence of sliding bifurcations. Through qualitative analysis, and based on the critical thresholds R0i(i=1,2), we elucidate the complex dynamics of the proposed model, including scenarios of monostable, bistable, or even tristable coexistence. Numerical simulations further explore the effects of key parameters related to the treatment strategies, demonstrating that media coverage, protective measures, and vaccination play pivotal roles in controlling the spread of the disease. Our findings indicate that by selecting appropriate threshold values, it is possible to effectively limit the peak number of infected individuals and the overall scale of the outbreak to a desired level. This provides a robust control strategy for managing emergent infectious diseases that cannot be immediately eradicated.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143975718","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

Optimal system of Lie subalgebras and exact solutions of a nonlinear elastic rod equation. 李子代数的最优系统及非线性弹性杆方程的精确解。

IF 2.7 2区数学

Chaos Pub Date : 2025-05-01 DOI: 10.1063/5.0254075

Supriya Mondal, Arindam Ghosh, Sarit Maitra

引用次数: 0

Density evolution in stochastic dynamical systems with memory: A universal algorithm. 具有记忆的随机动力系统的密度演化：一个通用算法。

IF 2.7 2区数学

Chaos Pub Date : 2025-05-01 DOI: 10.1063/5.0258144

Xianming Liu, Thomas Sun

引用次数: 0

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