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Global synchronization on time-varying higher-order structures 时变高阶结构上的全局同步
IF 2.7 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-03-21 DOI: 10.1088/2632-072x/ad3262
Md Sayeed Anwar, Dibakar Ghosh, Timoteo Carletti
Synchronization has received a lot of attention from the scientific community for systems evolving on static networks or higher-order structures, such as hypergraphs and simplicial complexes. In many relevant real-world applications, the latter are not static but do evolve in time, in this work we thus discuss the impact of the time-varying nature of higher-order structures in the emergence of global synchronization. To achieve this goal, we extend the master stability formalism to account, in a general way, for the additional contributions arising from the time evolution of the higher-order structure supporting the dynamical systems. The theory is successfully challenged against two illustrative examples, the Stuart–Landau nonlinear oscillator and the Lorenz chaotic oscillator.
对于在静态网络或高阶结构(如超图和简单复合物)上演化的系统,同步问题受到了科学界的广泛关注。在现实世界的许多相关应用中,后者并非静态,而是随时间演化的。因此,在这项工作中,我们将讨论高阶结构的时变性质对全局同步出现的影响。为了实现这一目标,我们扩展了主稳定性形式主义,以一般的方式解释支持动力系统的高阶结构的时间演化所产生的额外贡献。我们通过斯图尔特-朗道非线性振荡器和洛伦兹混沌振荡器这两个示例,成功挑战了这一理论。
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引用次数: 0
Nonuniformly twisted states and traveling chimeras in a system of nonlocally coupled identical phase oscillators 非局部耦合相同相位振荡器系统中的非均匀扭曲态和旅行嵌合体
IF 2.7 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-03-13 DOI: 10.1088/2632-072x/ad2ec2
L A Smirnov, M I Bolotov, A Pikovsky
We explore the model of a population of nonlocally coupled identical phase oscillators on a ring (Abrams and Strogatz 2004 Phys. Rev. Lett.93 174102) and describe traveling patterns. In the continuous in space formulation, we find families of traveling wave solutions for left-right symmetric and asymmetric couplings. Only the simplest of these waves are stable, which is confirmed by numerical simulations for a finite population. We demonstrate that for asymmetric coupling, a weakly turbulent traveling chimera regime is established, both from an initial standing chimera or an unstable traveling wave profile. The weakly turbulent chimera is a macroscopically chaotic state, with a well-defined synchronous domain and partial coherence in the disordered domain. We characterize it through the correlation function and the Lyapunov spectrum.
我们探讨了环上非局部耦合的相同相位振子群模型(Abrams 和 Strogatz 2004 Phys.在空间连续公式中,我们发现了左右对称和不对称耦合的行波解系列。只有最简单的行波是稳定的,这一点通过对有限群体的数值模拟得到了证实。我们证明,对于非对称耦合,弱湍流行波奇美拉机制是建立在初始静止奇美拉或不稳定行波剖面的基础上的。弱湍流奇美拉是一种宏观混沌状态,具有定义明确的同步域和无序域中的部分相干性。我们通过相关函数和李亚普诺夫频谱来描述它的特征。
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引用次数: 0
Mobility restrictions in response to local epidemic outbreaks in rock-paper-scissors models 在 "剪刀石头布 "模型中应对地方流行病爆发的流动限制
IF 2.7 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-03-08 DOI: 10.1088/2632-072x/ad2d5b
J Menezes
We study a three-species cyclic model whose organisms are vulnerable to contamination with an infectious disease which propagates person-to-person. We consider that individuals of one species perform a self-preservation strategy by reducing the mobility rate to minimise infection risk whenever an epidemic outbreak reaches the neighbourhood. Running stochastic simulations, we quantify the changes in spatial patterns induced by unevenness in the cyclic game introduced by the mobility restriction strategy of organisms of one out of the species. Our findings show that variations in disease virulence impact the benefits of dispersal limitation reaction, with the relative reduction of the organisms’ infection risk accentuating in surges of less contagious or deadlier diseases. The effectiveness of the mobility restriction tactic depends on the deceleration level and the fraction of infected neighbours which is considered too dangerous, thus triggering the defensive strategy. If each organism promptly reacts to the arrival of the first viral vectors in its surroundings with strict mobility reduction, contamination risk decreases significantly. Our conclusions may help biologists understand the impact of defensive strategies in ecosystems during an epidemic.
我们研究了一个三物种循环模型,该模型中的生物很容易受到人际传播的传染病的污染。我们认为,当流行病爆发到达邻近地区时,一个物种的个体会采取自我保护策略,降低流动率,从而将感染风险降到最低。通过随机模拟,我们量化了由其中一个物种的生物体的流动限制策略所带来的循环博弈中的不平衡性所引起的空间模式变化。我们的研究结果表明,疾病毒性的变化会影响限制扩散反应的益处,在传染性较弱或致命性较高的疾病激增时,生物体感染风险的相对降低会更加明显。流动限制策略的有效性取决于减速水平和被认为太危险的受感染邻居的比例,从而触发防御策略。如果每种生物都能在其周围出现第一批病毒载体时迅速做出反应,严格降低流动性,那么污染风险就会大大降低。我们的结论可能有助于生物学家理解流行病期间生态系统中防御策略的影响。
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引用次数: 0
Local sign stability and its implications for spectra of sparse random graphs and stability of ecosystems 局部符号稳定性及其对稀疏随机图谱和生态系统稳定性的影响
IF 2.7 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-03-06 DOI: 10.1088/2632-072x/ad2698
Pietro Valigi, Izaak Neri, Chiara Cammarota
We study the spectral properties of sparse random graphs with different topologies and type of interactions, and their implications on the stability of complex systems, with particular attention to ecosystems. Specifically, we focus on the behaviour of the leading eigenvalue in different type of random matrices (including interaction matrices and Jacobian-like matrices), relevant for the assessment of different types of dynamical stability. By comparing numerical results on Erdős–Rényi and Husimi graphs with sign-antisymmetric interactions or mixed sign patterns, we propose a sufficient criterion, called strong local sign stability, for stability not to be affected by system size, as traditionally implied by the complexity-stability trade-off in conventional models of random matrices. The criterion requires sign-antisymmetric or unidirectional interactions and a local structure of the graph such that the number of cycles of finite length do not increase with the system size. Note that the last requirement is stronger than the classical local tree-like condition, which we associate to the less stringent definition of local sign stability, also defined in the paper. In addition, for strong local sign stable graphs which show stability to linear perturbations irrespectively of system size, we observe that the leading eigenvalue can undergo a transition from being real to acquiring a nonnull imaginary part, which implies a dynamical transition from nonoscillatory to oscillatory linear response to perturbations. Lastly, we ascertain the discontinuous nature of this transition.
我们研究具有不同拓扑结构和相互作用类型的稀疏随机图的频谱特性,以及它们对复杂系统稳定性的影响,尤其关注生态系统。具体来说,我们关注不同类型随机矩阵(包括相互作用矩阵和雅各布类矩阵)中前导特征值的行为,这与评估不同类型的动态稳定性相关。通过比较具有符号不对称相互作用或混合符号模式的厄尔多斯-雷尼图和胡西米图的数值结果,我们提出了一个充分的标准,称为强局部符号稳定性,它使稳定性不受系统大小的影响,正如传统随机矩阵模型的复杂性-稳定性权衡所暗示的那样。该标准要求符号不对称或单向相互作用,以及图的局部结构,即有限长度的循环次数不随系统大小而增加。请注意,最后一个要求比经典的局部树状条件更强,我们将其与本文定义的局部符号稳定性这一较宽松的定义联系起来。此外,对于强局部符号稳定图,无论系统大小如何,都能表现出对线性扰动的稳定性,我们观察到前导特征值可以经历从实部到获得非零虚部的转变,这意味着对扰动的线性响应从非振荡到振荡的动态转变。最后,我们确定了这种过渡的不连续性。
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引用次数: 0
Pathways to discontinuous transitions in interacting contagion dynamics 在相互作用的传染动力学中实现不连续转换的途径
IF 2.7 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-02-28 DOI: 10.1088/2632-072x/ad269b
Santiago Lamata-Otín, Jesús Gómez-Gardeñes, David Soriano-Paños
Yet often neglected, dynamical interdependencies between concomitant contagion processes can alter their intrinsic equilibria and bifurcations. A particular case of interest for disease control is the emergence of discontinuous transitions in epidemic dynamics coming from their interactions with other simultaneous processes. To address this problem, here we propose a framework coupling a standard epidemic dynamics with another contagion process, presenting a tunable parameter shaping the nature of its transitions. Our model retrieves well-known results in the literature, such as the existence of first-order transitions arising from the mutual cooperation of epidemics or the onset of abrupt transitions when social contagions unidirectionally drive epidemics. We also reveal that negative feedback loops between simultaneous dynamical processes might suppress abrupt phenomena, thus increasing systems robustness against external perturbations. Our results render a general perspective toward finding different pathways to abrupt phenomena from the interaction of contagion processes.
然而,往往被忽视的是,同时发生的传染过程之间的动态相互依存关系会改变其内在平衡和分岔。对于疾病控制来说,一个特别值得关注的情况是,流行病动力学中出现的不连续转换来自于它们与其他同时发生的过程之间的相互作用。为了解决这个问题,我们在此提出了一个将标准流行病动力学与另一个传染过程耦合的框架,提出了一个可调参数来塑造其过渡的性质。我们的模型检索了文献中众所周知的结果,如流行病相互合作产生的一阶过渡的存在,或社会传染单向驱动流行病时突然过渡的发生。我们还揭示了同时发生的动态过程之间的负反馈回路可能会抑制突变现象,从而增强系统对外部扰动的稳健性。我们的研究结果提供了一个总体视角,有助于从传染过程的相互作用中找到产生突变现象的不同途径。
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引用次数: 0
Effects of topological structure and destination selection strategies on agent dynamics in complex networks 拓扑结构和目的地选择策略对复杂网络中代理动态的影响
IF 2.7 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-02-23 DOI: 10.1088/2632-072x/ad2971
Satori Tsuzuki, Daichi Yanagisawa, Eri Itoh, Katsuhiro Nishinari
We analyzed agent behavior in complex networks: Barabási–Albert, Erdos–Rényi, and Watts–Strogatz models under the following rules: agents (a) randomly select a destination among adjacent nodes; (b) exclude the most congested adjacent node as a potential destination and randomly select a destination among the remaining nodes; or (c) select the sparsest adjacent node as a destination. We focused on small complex networks with node degrees ranging from zero to a maximum of approximately 20 to study agent behavior in traffic and transportation networks. We measured the hunting rate, that is, the rate of change of agent amounts in each node per unit of time, and the imbalance of agent distribution among nodes. Our simulation study reveals that the topological structure of a network precisely determines agent distribution when agents perform full random walks; however, their destination selections alter the agent distribution. Notably, rule (c) makes hunting and imbalance rates significantly high compared with random walk cases (a) and (b), irrespective of network types, when the network has a high degree and high activity rate. Compared with the full random walk in (a) and (b) increases the hunting rate while decreasing the imbalance rate when activity is low; however, both increase when activity is high. These characteristics exhibit slight periodic undulations over time. Furthermore, our analysis shows that in the BA, ER, and WS network models, the hunting rate decreases and the imbalance rate increases when the system disconnects randomly selected nodes in simulations where agents follow rules (a)–(c) and the network has the ability to disconnect nodes within a certain time of all time steps. Our findings can be applied to various applications related to agent dynamics in complex networks.
我们分析了复杂网络中的代理行为:Barabási-Albert、Erdos-Rényi 和 Watts-Strogatz 模型的规则如下:代理(a)在相邻节点中随机选择一个目的地;(b)排除最拥挤的相邻节点作为潜在目的地,并在其余节点中随机选择一个目的地;或(c)选择最稀疏的相邻节点作为目的地。我们重点研究了节点度从零到最大约 20 度的小型复杂网络,以研究交通和运输网络中的代理行为。我们测量了狩猎率,即单位时间内每个节点上代理数量的变化率,以及代理在节点间分布的不平衡性。我们的模拟研究表明,当代理进行完全随机行走时,网络的拓扑结构精确地决定了代理的分布;然而,代理对目的地的选择改变了代理的分布。值得注意的是,与随机漫步情况(a)和(b)相比,无论网络类型如何,当网络具有高度和高活动率时,规则(c)都会使猎杀率和不平衡率显著提高。与完全随机漫步相比,(a)和(b)中的狩猎率会在活动量较低时增加,而失衡率会降低;但是,在活动量较高时,狩猎率和失衡率都会增加。这些特征随着时间的推移呈现出轻微的周期性起伏。此外,我们的分析表明,在 BA、ER 和 WS 网络模型中,在代理遵循(a)-(c)规则且网络有能力在所有时间步骤的一定时间内断开节点连接的模拟中,当系统断开随机选择的节点连接时,狩猎率会降低,不平衡率会增加。我们的研究结果可应用于与复杂网络中的代理动态相关的各种应用。
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引用次数: 0
Transfer operators on graphs: spectral clustering and beyond 图上的转移算子:频谱聚类及其他
IF 2.7 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-02-23 DOI: 10.1088/2632-072x/ad28fe
Stefan Klus, Maia Trower
Graphs and networks play an important role in modeling and analyzing complex interconnected systems such as transportation networks, integrated circuits, power grids, citation graphs, and biological and artificial neural networks. Graph clustering algorithms can be used to detect groups of strongly connected vertices and to derive coarse-grained models. We define transfer operators such as the Koopman operator and the Perron–Frobenius operator on graphs, study their spectral properties, introduce Galerkin projections of these operators, and illustrate how reduced representations can be estimated from data. In particular, we show that spectral clustering of undirected graphs can be interpreted in terms of eigenfunctions of the Koopman operator and propose novel clustering algorithms for directed graphs based on generalized transfer operators. We demonstrate the efficacy of the resulting algorithms on several benchmark problems and provide different interpretations of clusters.
图和网络在模拟和分析复杂的互连系统(如交通网络、集成电路、电网、引文图以及生物和人工神经网络)中发挥着重要作用。图聚类算法可用于检测强连接顶点群,并推导出粗粒度模型。我们定义了图上的 Koopman 算子和 Perron-Frobenius 算子等转移算子,研究了它们的频谱特性,引入了这些算子的 Galerkin 投影,并说明了如何从数据中估算简化表示。我们特别指出,无向图的谱聚类可以用 Koopman 算子的特征函数来解释,并提出了基于广义转移算子的有向图新聚类算法。我们在几个基准问题上演示了所产生的算法的有效性,并提供了对聚类的不同解释。
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引用次数: 0
Strength of minority ties: the role of homophily and group composition in a weighted social network 少数群体联系的强度:加权社会网络中同亲关系和群体构成的作用
IF 2.7 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-02-16 DOI: 10.1088/2632-072x/ad2720
José R Nicolás-Carlock, Denis Boyer, Sandra E Smith-Aguilar, Gabriel Ramos-Fernández
Homophily describes a fundamental tie-formation mechanism in social networks in which connections between similar nodes occur at a higher rate than among dissimilar ones. In this article, we present an extension of the weighted social network (WSN) model that, under an explicit homophily principle, quantifies the emergence of attribute-dependent properties of a social system. To test our model, we make use of empirical association data of a group of free-ranging spider monkeys in Yucatan, Mexico. Our homophilic WSN model reproduces many of the properties of the empirical association network with statistical significance, specifically, the average weight of sex-dependent interactions (female-female, female-male, male-male), the weight distribution function, as well as many weighted macro properties (node strength, weighted clustering, and weighted number of modules), even for different age group combinations (adults, subadults, and juveniles). Furthermore, by performing simulations with fitted parameters, we show that one of the main features of a spider monkey social system, namely, stronger male-male interactions over female-female or female-male ones, can be accounted for by an asymmetry in the node-type composition of a bipartisan network, independently of group size. The reinforcement of connections among members of minority groups could be a general structuring mechanism in homophilic social networks.
同质性(Homophily)描述了社会网络中的一种基本纽带形成机制,即相似节点之间的连接发生率高于不同节点之间的连接发生率。在本文中,我们对加权社会网络(WSN)模型进行了扩展,在明确的同亲原则下,对社会系统中出现的依赖于属性的特性进行了量化。为了检验我们的模型,我们利用了墨西哥尤卡坦半岛一群自由活动的蜘蛛猴的经验关联数据。我们的嗜同性 WSN 模型重现了经验关联网络的许多属性,并具有统计学意义,特别是与性别相关的相互作用(雌-雌、雌-雄、雄-雄)的平均权重、权重分布函数以及许多加权宏观属性(节点强度、加权聚类和加权模块数),甚至对不同年龄组组合(成年、亚成年和幼年)也是如此。此外,通过使用拟合参数进行模拟,我们发现蜘蛛猴社会系统的一个主要特征,即雄性与雄性之间的互动强于雌性与雌性之间或雌性与雄性之间的互动,可以通过两党网络节点类型组成的不对称性来解释,而与群体大小无关。少数群体成员之间联系的加强可能是同亲社会网络的一般结构机制。
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引用次数: 0
The complexity of climate change mitigation: an experiment with large groups 减缓气候变化的复杂性:大型团体实验
IF 2.7 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-02-14 DOI: 10.1088/2632-072x/ad2372
Antonio Alfonso, Pablo Brañas-Garza, Antonio Cabrales, Angel Sánchez
We have studied the problem of climate change mitigation in large groups by means of a series of experiments with 1785 people. Our participants included both young university students and people of relevance in different organizations, in particular, those attending the presentation of the annual report on innovation by Fundación COTEC (Spain). In the experiment, the participants, distributed in groups of more than 100 people, faced a dilemma: to avoid a global catastrophe that destroys any possibility of making profits, a certain collective sacrifice has to be made by contributing to reach a global threshold. When the threshold was low, the students reached the amount of overall contribution necessary to avoid it. But in the case of a high threshold, none of the populations reached the threshold. In fact, they were far from it. In this sense, the collective behavior of the students and of people of relevance was fundamentally the same. The majority of participants in the high-risk case fell into four categories: those who did not contribute (around 10%), those who contribute half of their means (15%) but less than the fair share required to reach the threshold, those who contributed the fair share (10%), and those who contributed everything they had, so that their personal benefit was zero. In the case of students this last percentage was 10%, but in the other sample it reached almost 30%. We also found that individuals could be classified as being optimistic or pessimistic, and in general they behaved accordingly with regard to their contributions. Our results highlight the complexity of mitigating climate change in large groups and specially the difficulty in communicating the issue to foster action in a general population.
我们通过一系列有 1785 人参加的实验,研究了在大型群体中减缓气候变化的问题。我们的参与者既有年轻的大学生,也有不同组织的相关人员,特别是参加 COTEC 基金会(西班牙)年度创新报告发布会的人员。在实验中,参与者分成了 100 多人的小组,他们面临着一个两难的选择:为了避免一场全球性灾难破坏任何盈利的可能性,必须做出一定的集体牺牲,贡献力量以达到一个全球性的临界值。当阈值较低时,学生们达到了避免灾难所需的总体捐款额。但在门槛较高的情况下,没有一个人达到门槛。事实上,他们离阈值还很远。从这个意义上说,学生和相关人员的集体行为是基本相同的。高风险情况下的大多数参与者可分为四类:不缴费者(约 10%)、缴费额为其收入的 一半(15%)但少于达到门槛所需的公平份额者、缴费额为公平份额者(10%)和缴费额 为其所有但个人收益为零者。在学生中,最后这一比例为 10%,但在其他样本中,这一比例几乎达到了 30%。我们还发现,个人可分为乐观型和悲观型,一般来说,他们的贡献行为也是如此。我们的研究结果凸显了在大型群体中减缓气候变化的复杂性,特别是在普通人群中宣传这一问题以促进行动的难度。
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引用次数: 0
Filtering higher-order datasets 筛选高阶数据集
IF 2.7 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-02-13 DOI: 10.1088/2632-072x/ad253a
Nicholas W Landry, Ilya Amburg, Mirah Shi, Sinan G Aksoy
Many complex systems often contain interactions between more than two nodes, known as higher-order interactions, which can change the structure of these systems in significant ways. Researchers often assume that all interactions paint a consistent picture of a higher-order dataset’s structure. In contrast, the connection patterns of individuals or entities in empirical systems are often stratified by interaction size. Ignoring this fact can aggregate connection patterns that exist only at certain scales of interaction. To isolate these scale-dependent patterns, we present an approach for analyzing higher-order datasets by filtering interactions by their size. We apply this framework to several empirical datasets from three domains to demonstrate that data practitioners can gain valuable information from this approach.
许多复杂系统往往包含两个以上节点之间的交互作用,即所谓的高阶交互作用,这些交互作用会显著改变这些系统的结构。研究人员通常认为,所有的交互作用都会对高阶数据集的结构产生一致的影响。与此相反,经验系统中个体或实体的连接模式往往因交互大小而分层。如果忽略这一事实,就会汇总只存在于特定互动规模的连接模式。为了分离出这些与规模相关的模式,我们提出了一种通过筛选互动规模来分析高阶数据集的方法。我们将这一框架应用于三个领域的几个经验数据集,以证明数据从业者可以从这种方法中获得有价值的信息。
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引用次数: 0
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Journal of Physics Complexity
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