Chaos最新文献_第3页

Constraining safe and unsafe overshoots in saddle-node bifurcations.

IF 2.7 2区数学

Chaos Pub Date : 2025-01-01 DOI: 10.1063/5.0197940

Elias Enache, Oleksandr Kozak, Nico Wunderling, Jürgen Vollmer

{"title":"Constraining safe and unsafe overshoots in saddle-node bifurcations.","authors":"Elias Enache, Oleksandr Kozak, Nico Wunderling, Jürgen Vollmer","doi":"10.1063/5.0197940","DOIUrl":"https://doi.org/10.1063/5.0197940","url":null,"abstract":"We consider a dynamical system undergoing a saddle-node bifurcation with an explicitly time-dependent parameter p(t). The combined dynamics can be considered a dynamical system where p is a slowly evolving parameter. Here, we investigate settings where the parameter features an overshoot. It crosses the bifurcation threshold for some finite duration te and up to an amplitude R, before it returns to its initial value. We denote the overshoot as safe when the dynamical system returns to its initial state. Otherwise, one encounters runaway trajectories (tipping), and the overshoot is unsafe. For shallow overshoots (small R), safe and unsafe overshoots are discriminated by an inverse square-root border, te∝R-1/2, as reported in earlier literature. However, for larger overshoots, we here establish a crossover to another power law with an exponent that depends on the asymptotics of p(t). For overshoots with a finite support, we find that te∝R-1, and we provide examples for overshoots with exponents in the range [-1,-1/2]. All results are substantiated by numerical simulations, and it is discussed how the analytic and numeric results pave the way toward improved risk assessments separating safe from unsafe overshoots in climate, ecology, and nonlinear dynamics.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143051840","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

Studying power-grid synchronization with incremental refinement of model heterogeneity. 基于模型异质性增量细化的电网同步研究。

IF 2.7 2区数学

Chaos Pub Date : 2025-01-01 DOI: 10.1063/5.0237050

B Hartmann, G Ódor, K Benedek, I Papp

{"title":"Studying power-grid synchronization with incremental refinement of model heterogeneity.","authors":"B Hartmann, G Ódor, K Benedek, I Papp","doi":"10.1063/5.0237050","DOIUrl":"https://doi.org/10.1063/5.0237050","url":null,"abstract":"The dynamics of electric power systems are widely studied through the phase synchronization of oscillators, typically with the use of the Kuramoto equation. While there are numerous well-known order parameters to characterize these dynamics, shortcoming of these metrics are also recognized. To capture all transitions from phase disordered states over phase locking to fully synchronized systems, new metrics were proposed and demonstrated on homogeneous models. In this paper, we aim to address a gap in the literature, namely, to examine how the gradual improvement of power grid models affects the goodness of certain metrics. To study how the details of models are perceived by the different metrics, 12 variations of a power grid model were created, introducing varying levels of heterogeneity through the coupling strength, the nodal powers, and the moment of inertia. The grid models were compared using a second-order Kuramoto equation and adaptive Runge-Kutta solver, measuring the values of the phase, the frequency, and the universal order parameters. Finally, frequency results of the models were compared to grid measurements. We found that the universal order parameter was able to capture more details of the grid models, especially in cases of decreasing moment of inertia. Even the most heterogeneous models showed notable synchronization, encouraging the use of such models. Finally, we show local frequency results related to the multi-peaks of static models, which implies that spatial heterogeneity can also induce such multi-peak behavior.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143001083","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

Reliable detection of directional couplings using cross-vector measures. 使用交叉矢量测量可靠地检测方向耦合。

IF 2.7 2区数学

Chaos Pub Date : 2025-01-01 DOI: 10.1063/5.0238375

Martin Brešar, Ralph G Andrzejak, Pavle Boškoski

{"title":"Reliable detection of directional couplings using cross-vector measures.","authors":"Martin Brešar, Ralph G Andrzejak, Pavle Boškoski","doi":"10.1063/5.0238375","DOIUrl":"https://doi.org/10.1063/5.0238375","url":null,"abstract":"Detecting directional couplings from time series is crucial in understanding complex dynamical systems. Various approaches based on reconstructed state-spaces have been developed for this purpose, including a cross-distance vector measure, which we introduced in our recent work. Here, we devise two new cross-vector measures that utilize ranks and time series estimates instead of distances. We analyze various deterministic and stochastic dynamics to compare our cross-vector approach against some established state-space-based approaches. We demonstrate that all three cross-vector measures can identify the correct coupling direction for a broader range of couplings for all considered dynamics. Among the three cross-vector measures, the rank-based variant performs the best. Comparing this novel measure to an established rank-based measure confirms that it is more noise-robust and less affected by linear cross-correlation. To extend this comparison to real-world signals, we combine both measures with the method of surrogates and analyze a database of electroencephalographic (EEG) recordings from epilepsy patients. This database contains signals from brain areas where the patients' seizures were detected first and signals from brain areas that were not involved in the seizure onset. A better discrimination between these signal classes is obtained by the cross-rank vector measure. Additionally, this measure proves to be robust to non-stationarity, as its results remain nearly unchanged when the analysis is repeated for the subset of EEG signals that were identified as stationary in previous work. These findings suggest that the cross-vector approach can serve as a valuable tool for researchers analyzing complex time series and for clinical applications.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142962121","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

Novel patterns in discrete Ikeda map: Quint points and complex non-quantum chirality. 离散池田映射中的新模式：Quint点和复非量子手性。

IF 2.7 2区数学

Chaos Pub Date : 2025-01-01 DOI: 10.1063/5.0233735

Zeyi Liu, Xingzhao Guo, Xiaobo Rao

引用次数: 0

Reconstructing attractors with autoencoders. 用自编码器重构吸引子。

IF 2.7 2区数学

Chaos Pub Date : 2025-01-01 DOI: 10.1063/5.0232584

F Fainstein, G B Mindlin, P Groisman

引用次数: 0

Symbolic dynamics of joint brain states during dyadic coordination. 二元协调过程中关节脑状态的符号动力学。

IF 2.7 2区数学

Chaos Pub Date : 2025-01-01 DOI: 10.1063/5.0234902

Italo Ivo Lima Dias Pinto, Zhibin Zhou, Javier Omar Garcia, Ramesh Srinivasan

{"title":"Symbolic dynamics of joint brain states during dyadic coordination.","authors":"Italo Ivo Lima Dias Pinto, Zhibin Zhou, Javier Omar Garcia, Ramesh Srinivasan","doi":"10.1063/5.0234902","DOIUrl":"10.1063/5.0234902","url":null,"abstract":"We propose a novel approach to investigate the brain mechanisms that support coordination of behavior between individuals. Brain states in single individuals defined by the patterns of functional connectivity between brain regions are used to create joint symbolic representations of brain states in two or more individuals to investigate symbolic dynamics that are related to interactive behaviors. We apply this approach to electroencephalographic data from pairs of subjects engaged in two different modes of finger-tapping coordination tasks (synchronization and syncopation) under different interaction conditions (uncoupled, leader-follower, and mutual) to explore the neural mechanisms of multi-person motor coordination. Our results reveal that dyads exhibit mostly the same joint symbols in different interaction conditions-the most important differences are reflected in the symbolic dynamics. Recurrence analysis shows that interaction influences the dwell time in specific joint symbols and the structure of joint symbol sequences (motif length). In synchronization, increasing feedback promotes stability with longer dwell times and motif length. In syncopation, leader-follower interactions enhance stability (increase dwell time and motif length), but mutual interaction dramatically reduces stability. Network analysis reveals distinct topological changes with task and feedback. In synchronization, stronger coupling stabilizes a few states, preserving a core-periphery structure of the joint brain states while in syncopation we observe a more distributed flow amongst a larger set of joint brain states. This study introduces symbolic representations of metastable joint brain states and associated analytic tools that have the potential to expand our understanding of brain dynamics in human interaction and coordination.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142920873","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

Aging in a weighted ensemble of excitable and self-oscillatory neurons: The role of pairwise and higher-order interactions. 可兴奋和自振荡神经元加权集合中的衰老：成对和高阶相互作用的作用。

IF 2.7 2区数学

Chaos Pub Date : 2025-01-01 DOI: 10.1063/5.0247769

Amit Sharma, Biswambhar Rakshit, Kazuyuki Aihara

引用次数: 0

Inverse stochastic resonance in a two-dimensional airfoil system with nonlinear pitching stiffness driven by Lévy noise. 基于l<s:1>杂波噪声驱动的非线性俯仰刚度二维翼型系统逆随机共振。

IF 2.7 2区数学

Chaos Pub Date : 2025-01-01 DOI: 10.1063/5.0244641

Jinjie Zhu, Xianbin Liu

引用次数: 0

Discovering stochastic basin stability from data in a Filippov competition system with threshold control. 从具有阈值控制的Filippov竞争系统数据中发现随机流域稳定性。