Chaos最新文献 - Book学术

General oblique projections for model reduction via spectral submanifolds. 通过谱子流形进行模型简化的一般斜投影。

IF 3.2 2区数学

Chaos Pub Date : 2026-05-01 DOI: 10.1063/5.0319241

Leonardo Bettini, Amirhossein Kazemipour, Robert K Katzschmann, George Haller

引用次数: 0

Is the classical Rössler attractor periodic? A validated numerical study. 经典的Rössler吸引子是周期性的吗？经过验证的数值研究。

IF 3.2 2区数学

Chaos Pub Date : 2026-05-01 DOI: 10.1063/5.0301581

Zbigniew Galias

引用次数: 0

Toward a new generation of market indicators driven by blockchain transaction networks. 迈向由区块链交易网络驱动的新一代市场指标。

IF 3.2 2区数学

Chaos Pub Date : 2026-05-01 DOI: 10.1063/5.0307162

Mar Grande, Sergio Gómez, Florentino Borondo, Javier Borondo

{"title":"Toward a new generation of market indicators driven by blockchain transaction networks.","authors":"Mar Grande, Sergio Gómez, Florentino Borondo, Javier Borondo","doi":"10.1063/5.0307162","DOIUrl":"https://doi.org/10.1063/5.0307162","url":null,"abstract":"Cryptocurrencies and Decentralized Finance (DeFi) currently represent a fast growing trend in finance, which enables financial services on public blockchains. In contrast to traditional financial markets, ruled by well established corporations, DeFi is completely transparent, as it keeps publicly available records of all transactions that occur in the network. This availability of the data represents an opportunity to analyze and understand the market from the point of view of the complexity that emerges from the interactions among actors (users, bots, and companies) operating in the embedded market. In this paper, we focus on Ethereum to show that the underlying transaction network bears further and useful information to forecast the evolution of the market. We aim to separate the non-redundant effects of the blockchain transaction network from technical analysis and social media trends in the future price of the Ethereum native cryptocurrency. To this end, we build two machine learning models to predict the future trend of the price time series. The first model, serving as a base, considers the set of most relevant features according to the current scientific literature-including technical analysis and social media trends. The second model considers the features of the base model, incorporating the network properties computed from the transaction network. We find that the second model outperforms the base model and can anticipate 46% more rises in the price than the base model and 19% more falls. Thus, we conclude that new indicators based on network properties provide valuable information to forecast the future direction of the market that cannot be explained neither by technical analysis nor by social media trends alone. Hence, our results represent an important first step toward the definition of a new family of DeFi market indicators based on the complexity of the underlying transaction network.","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":"147834298","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

Two sufficient conditions for altering algebraic connectivity via edge addition in single-root digraphs. 单根有向图中边加法改变代数连通性的两个充分条件。

IF 3.2 2区数学

Chaos Pub Date : 2026-05-01 DOI: 10.1063/5.0319682

Run Zou, Yihui Wang, Xiaojing Zhu, Quanjun Wu

{"title":"Two sufficient conditions for altering algebraic connectivity via edge addition in single-root digraphs.","authors":"Run Zou, Yihui Wang, Xiaojing Zhu, Quanjun Wu","doi":"10.1063/5.0319682","DOIUrl":"https://doi.org/10.1063/5.0319682","url":null,"abstract":"This paper studies how adding an edge affects the second smallest eigenvalue λ2 of the Laplacian matrix in single-root digraphs, aiming to determine whether such an addition increases, decreases, or leaves λ2 unchanged. First, a spectral framework built via the block lower-triangular decomposition induced by strongly connected components (SCCs) to distinguish each SCC's contribution to the overall spectrum enables the establishment of two sufficient conditions using matrix perturbation theory, adjugate-matrix identities, and properties of irreducible M-matrices. Specifically, when the algebraic multiplicity of λ2 is one, these two conditions serve as criteria for the change in λ2: The first corresponds to cases of increase or no change and the second to cases of a strict decrease. Second, it is shown that when the algebraic multiplicity of λ2 exceeds one, λ2 can remain invariant under specific structural constraints on the added edge. Finally, numerical simulations on Erdős-Rényi and scale-free networks validate the theoretical criteria and reveal topology-dependent variations in the magnitude of change in λ2. Furthermore, applications to Kuramoto oscillator networks demonstrate that edge additions predicted to decrease λ2 lead to slower synchronization, confirming the dynamical significance of the proposed spectral conditions.","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":"147834353","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

Event-triggered pinning synchronization of stochastic complex networks under hybrid attacks. 混合攻击下随机复杂网络的事件触发钉钉同步。

IF 3.2 2区数学

Chaos Pub Date : 2026-05-01 DOI: 10.1063/5.0328204

Hailan Yang, Guohua Wu, Huimin Wang, Guanghui Wen, Yongzheng Sun

{"title":"Event-triggered pinning synchronization of stochastic complex networks under hybrid attacks.","authors":"Hailan Yang, Guohua Wu, Huimin Wang, Guanghui Wen, Yongzheng Sun","doi":"10.1063/5.0328204","DOIUrl":"https://doi.org/10.1063/5.0328204","url":null,"abstract":"This paper proposes a novel pinning event-triggered control protocol for resilient synchronization of complex networks under hybrid Denial-of-Service (DoS) and False Data Injection (FDI) attacks. By integrating pinning control with an event-triggered mechanism, the proposed protocol achieves global synchronization by actuating only a subset of nodes, significantly reducing communication and computational overhead. The frequency and duration constraints of non-periodic, asynchronous DoS attacks across different network boundaries are rigorously characterized, and the adverse effects of FDI attacks on synchronization are systematically quantified. To address the additional challenge of random noise in practical environments, a stochastic version of the protocol is developed, with theoretical guarantees ensuring synchronization is preserved under noisy conditions. Furthermore, the proposed event-triggering scheme is proven to be free of Zeno behavior. Numerical simulations validate the theoretical results and demonstrate that the proposed protocol achieves reliable synchronization under hybrid cyber-attacks and stochastic disturbances with reduced communication overhead.","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":"147833745","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

Time delay induced stochastic dynamics in a strongly nonlinear energy harvesting system. 强非线性能量收集系统的时滞随机动力学。

IF 3.2 2区数学

Chaos Pub Date : 2026-05-01 DOI: 10.1063/5.0335813

Yanxia Zhang, Shaoyi Shi, Yanfei Jin

{"title":"Time delay induced stochastic dynamics in a strongly nonlinear energy harvesting system.","authors":"Yanxia Zhang, Shaoyi Shi, Yanfei Jin","doi":"10.1063/5.0335813","DOIUrl":"https://doi.org/10.1063/5.0335813","url":null,"abstract":"Considering the unavoidable time delay effects and ubiquitous environmental noise in practical applications, along with the strong nonlinearity and multiple couplings inherent in actual systems, the resulting dynamical behavior becomes extremely complex, necessitating the development of new theoretical research methods. In this paper, a strongly nonlinear energy harvesting system with time delay is taken as the research object. To address the above difficulties, an extended stochastic averaging method is proposed to investigate the time delay induced stochastic dynamics of the system. The energy-dependent frequency is first constructed according to the operating mechanism of the multi-well potential function. Then, the stochastic averaging method of energy envelope is extended to derive analytical expressions for the stationary probability density and the mean output power. Finally, the effects of time delay parameters on the stationary response and the mean output power are analyzed in detail. Results show that even small time delays cannot be ignored in practical applications, as both the time-delayed feedback gain and the time delay have significant influences on the dynamic characteristics of systems. Moreover, adopting appropriate time-delayed feedback control can markedly enhance system performance. The effectiveness of the extended stochastic averaging method is verified through Monte Carlo numerical simulations.","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":"147834053","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

On the attractor in high-dimensional neural network dynamics of reservoir computing: A Lyapunov analysis viewpoint. 油藏计算高维神经网络动力学中的吸引子：李亚普诺夫分析观点。

IF 3.2 2区数学

Chaos Pub Date : 2026-05-01 DOI: 10.1063/5.0315384

Miki U Kobayashi, Kengo Nakai, Yoshitaka Saiki, Natsuki Tsutsumi

{"title":"On the attractor in high-dimensional neural network dynamics of reservoir computing: A Lyapunov analysis viewpoint.","authors":"Miki U Kobayashi, Kengo Nakai, Yoshitaka Saiki, Natsuki Tsutsumi","doi":"10.1063/5.0315384","DOIUrl":"https://doi.org/10.1063/5.0315384","url":null,"abstract":"Recent theoretical studies on reservoir computing have shown that when the spectral radius of the adjacency matrix is sufficiently small, the dynamics of a reference system can be embedded in the reservoir space, enabling the reconstruction of dynamical invariants. However, reservoir models often reproduce time series accurately even when the spectral radius is relatively large, where the underlying mechanism is not well understood. In this study, we investigate the reconstruction of dynamical structures from the perspective of Lyapunov analysis using reservoir computing applied to the Hénon map. By comparing the Lyapunov spectrum of the reservoir dynamics with that of the reference system, we show that the reference dynamics are embedded in a low-dimensional inertial manifold in the reservoir space. We further demonstrate that the full Lyapunov spectrum of the reference system can be recovered by restricting the analysis to the tangent space of this manifold, even when the spectral radius is relatively large. These results clarify the geometric mechanism underlying the successful reconstruction of chaotic dynamics by reservoir computing beyond the regime where theoretical guarantees currently exist.","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":"147834112","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

Rumor propagation and supervision during confrontation: An importance-driven SIRQS network model. 对抗中的谣言传播与监督：一个重要性驱动的SIRQS网络模型。

IF 3.2 2区数学

Chaos Pub Date : 2026-05-01 DOI: 10.1063/5.0336448

Wenjie Zhang, Juan Wu, Minyu Feng, Qin Li, Matjaž Perc

{"title":"Rumor propagation and supervision during confrontation: An importance-driven SIRQS network model.","authors":"Wenjie Zhang, Juan Wu, Minyu Feng, Qin Li, Matjaž Perc","doi":"10.1063/5.0336448","DOIUrl":"https://doi.org/10.1063/5.0336448","url":null,"abstract":"The societal impact of rumor spreading is becoming increasingly severe; yet, current research remains relatively one-sided, typically focusing on either rumor propagation or rumor control while neglecting the confrontational and dynamically evolving relationship between them. To address this gap, we propose a novel confrontation framework for rumor modeling. We extend the classical susceptible-infected-recovered-susceptible (SIRS) model into an ignorant-spreader-stifler-vigilant-ignorant (SIRQS) framework by introducing a vigilant state and a confrontation mechanism, thereby capturing subtle differences in individual states during rumor propagation and in their confrontational behavior toward supervisors. At the same time, supervisors patrol the network through random walks guided by node propagation importance, enabling targeted monitoring of rumor spreaders and individuals with a high risk of spreading rumors. Using a microscopic Markov chain approach, we further characterize heterogeneous node behavior and individual differences, and couple the propagation and supervision processes to model node-state transition patterns. We conduct simulations on networks with three different sizes, various topologies, and a real-world network. The results show that the supervision subject, the preference effects associated with the number of supervisors, and the confrontation mechanism are key factors in supervision, and largely determine the effectiveness of rumor propagation control in the simulations, reflecting the substantial influence of these three mechanisms in real-world spreading scenarios. Finally, through multiple evaluation indicators, we provide references for determining the optimal number of supervisors.","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":"147811627","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

Structure of memory in time series: A one-dimensional atomic chain model. 时间序列中的存储器结构：一维原子链模型。

IF 3.2 2区数学

Chaos Pub Date : 2026-05-01 DOI: 10.1063/5.0322841

Xiujiang Li, Quankun Zhao, Haiying Wang, Changgui Gu, Huijie Yang

{"title":"Structure of memory in time series: A one-dimensional atomic chain model.","authors":"Xiujiang Li, Quankun Zhao, Haiying Wang, Changgui Gu, Huijie Yang","doi":"10.1063/5.0322841","DOIUrl":"https://doi.org/10.1063/5.0322841","url":null,"abstract":"In current time series analysis, the structure of memory is lost. A concept called memory structure network is proposed to preserve the memory details. From the time series, one extracts all the possible segments, maps them each to nodes, and assigns the dependence between the node pairs to their corresponding edges as weights. The adjacency matrix for the resulting network is identical with the Hamiltonian for an electron walking along a one-dimensional lattice, with the help of which the memory is represented in a multi-dimensional space spanned by the spectral properties for the adjacency matrix. The behaviors for the index series of the Shanghai Stock Exchange Composite are shown and compared with that for the fractional Brownian motion (fBm) and the Autoregressive Conditional Heteroskedasticity (ARCH) models. The spectral distribution follows perfectly the beta-distribution and its skew increases monotonically with the Hurst exponent, which can (cannot) be reproduced with the fBm (ARCH) model. For the empirical and modeling series, the full spectra expose stronger repulsion effect due to the intrinsic mirror symmetry, while the symmetry-resolved sub-spectra obey the Weibull distribution and the repulsion effect increases monotonically with the long-term persistence and the fluctuation of variance. In addition, the rigidities for the symmetry-resolved sub-spectra are between the Poisson-like and the Gaussian orthogonal ensemble ones, while that for the full spectra are not sensitive to the difference in time series. This approach may answer the questions such as what a specific value of H means for the memory from the viewpoint of spectral behaviors.","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":"147811641","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

New insights into chaos in Rulkov map. 对Rulkov地图混乱的新见解。

IF 3.2 2区数学

Chaos Pub Date : 2026-05-01 DOI: 10.1063/5.0309109

Ruipeng Zhou, Hongjun Cao

{"title":"New insights into chaos in Rulkov map.","authors":"Ruipeng Zhou, Hongjun Cao","doi":"10.1063/5.0309109","DOIUrl":"https://doi.org/10.1063/5.0309109","url":null,"abstract":"The Rulkov map has been widely employed to mimic the bursting and spiking behaviors of biological neurons, offering both biological relevance and mathematical tractability. In this paper, a new formulation of the Rulkov fast subsystem is introduced by incorporating the fixed-point information (x∗,y∗)=(σ,σ-α1+σ2) of the original map. This auxiliary one-dimensional system, while not capturing the full two-dimensional dynamics, provides a mathematically transparent framework for rigorously analyzing the mechanisms underlying complex behaviors near the trivial fixed point. The local stability and bifurcation properties of this new fast subsystem are analyzed, revealing how the number and stability of fixed points evolve as the control parameters α and σ vary, and these findings are corroborated by numerical simulations. Using inverse mapping techniques, explicit parameter conditions are identified under which the fixed point x∗=σ serves as a snap-back repeller, thereby confirming the existence of chaos via Marotto's theorem. More importantly, going beyond the existence of chaos, we rigorously prove that the new fast subsystem contains periodic points of every positive integer period. This result not only aligns with the periodic windows observed in numerical bifurcation diagrams but also establishes a fundamental property of the system's dynamical complexity: the coexistence of infinitely many periodic orbits with all possible periods provides analytical evidence of the rich structure underlying the chaotic dynamics. These findings offer new analytical insights into the Rulkov map, complementing existing numerical studies and deepening the mathematical understanding of chaos in neuron models.","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":"147834141","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