Physica A: Statistical Mechanics and its Applications最新文献_第10页

Improving community detection in blockmodel by distance-based observation selection 通过基于距离的观测选择改进块模型中的群落检测

IF 2.8 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physica A: Statistical Mechanics and its Applications

Pub Date : 2024-09-24 DOI: 10.1016/j.physa.2024.130125

Cunqi Shao , Mincheng Wu , Shibo He

Community detection is an important research topic in complex systems and has plenty of applications in real-world networks. Probabilistic methods, such as the Expectation–Maximization (EM), are developed to classify nodes that have similar connection patterns in a network based on blockmodels. However, the detection procedures in these models are typically started from randomly generated initial community distributions without prior knowledge. In biological and social networks, there are practical measures to obtain prior knowledge for a subset of nodes, such as local observations. These facts lead us to question how we can select a subset of nodes with known community labels to enhance the accuracy of the EM method. The current selection methods lack the relationship between detection accuracy and structural characteristics and most approaches consider the nodes as the center of communities, which is not suitable for block models. In this paper, we first study the relationships between the structural distance and detection accuracy without prior knowledge. Then we propose a distance-based indicator to describe the performance of the observation node set in the EM method. Finally, we introduce a scoring method based on the indicator to select a partial observation set, improving the accuracy of community detection using the EM method. Empirical results from synthetic and real-world networks corroborate that the proposed indicator could contribute to a better performance in kinds of scenarios.

群落检测是复杂系统中的一个重要研究课题，在现实世界的网络中有大量应用。人们开发了一些概率方法，如期望最大化法（EM），用于根据块模型对网络中具有相似连接模式的节点进行分类。然而，这些模型中的检测程序通常是从随机生成的初始群落分布开始的，没有先验知识。在生物和社会网络中，有一些实用的方法可以获得节点子集的先验知识，例如局部观测。这些事实引发了我们的疑问：如何选择具有已知社区标签的节点子集，以提高 EM 方法的准确性？目前的选择方法缺乏检测精度与结构特征之间的关系，而且大多数方法都将节点视为群落的中心，这并不适合块模型。在本文中，我们首先研究了结构距离与检测精度之间的关系，而不需要先验知识。然后，我们提出了一种基于距离的指标来描述 EM 方法中观测节点集的性能。最后，我们引入了一种基于该指标的评分方法来选择部分观测集，从而提高使用 EM 方法进行群落检测的准确性。来自合成网络和真实世界网络的经验结果证实，所提出的指标在各种情况下都能帮助提高性能。

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引用次数: 0

Influence of initiators on the tipping point in the extended Watts model 扩展瓦特模型中启动器对临界点的影响

IF 2.8 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physica A: Statistical Mechanics and its Applications

Pub Date : 2024-09-24 DOI: 10.1016/j.physa.2024.130123

Takehisa Hasegawa, Shinji Nishioka

In this paper, we study how the influence of initiators (seeds) affects the tipping point of information cascades in networks. We consider an extended version of the Watts model, in which each node is either active (i.e., having adopted an innovation) or inactive. In this extended model, the adoption threshold, defined as the fraction of active neighbors required for an inactive node to become active, depends on whether the node is a seed neighbor (i.e., connected to one or more initiators) or an ordinary node (i.e., not connected to any initiators). Using the tree approximation on random graphs, we determine the tipping point, at which the fraction of active nodes in the final state increases discontinuously with an increasing seed fraction. The occurrence of a tipping point and the scale of cascades depend on two factors: whether a giant component of seed neighbors is formed when the seed fraction is large enough to trigger cascades among seed neighbors, and whether the giant component of ordinary nodes is maintained when newly activated nodes trigger further activations among ordinary nodes. The coexistence of two giant components suggests that a tipping point can appear twice. We present an example demonstrating the existence of two tipping points when there is a gap between the adoption thresholds of seed neighbors and ordinary nodes. Monte Carlo simulations clearly show that the first cascade, occurring at a small tipping point, occurs in the giant component of seed neighbors, while the second cascade, occurring at a larger tipping point, extends into the giant component of ordinary nodes.

本文研究了发起者（种子）的影响力如何影响网络中信息级联的临界点。我们考虑了沃茨模型的扩展版本，其中每个节点要么是活跃的（即采用了创新），要么是不活跃的。在这个扩展模型中，采用阈值被定义为不活跃节点变得活跃所需的活跃邻居的分数，它取决于该节点是种子邻居（即与一个或多个发起者相连）还是普通节点（即与任何发起者都不相连）。利用随机图上的树状近似，我们确定了临界点，在临界点上，最终状态中活跃节点的比例会随着种子比例的增加而不连续地增加。临界点的出现和级联的规模取决于两个因素：当种子分数大到足以引发种子邻居之间的级联时，是否会形成种子邻居的巨大分量；当新激活的节点引发普通节点之间的进一步激活时，是否会维持普通节点的巨大分量。两种巨型成分的共存表明，临界点可能会出现两次。我们举例说明，当种子邻居和普通节点的采用阈值之间存在差距时，就会出现两个临界点。蒙特卡洛模拟清楚地表明，在小临界点出现的第一次级联发生在种子邻居的巨大分量中，而在较大临界点出现的第二次级联延伸到普通节点的巨大分量中。

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引用次数: 0

On the kinetic temperature of a one-dimensional crystal on the long-time scale 论一维晶体的长时间尺度动力学温度

IF 2.8 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physica A: Statistical Mechanics and its Applications

Pub Date : 2024-09-24 DOI: 10.1016/j.physa.2024.130114

A.A. Lykov , A.S. Murachev

We investigate the dynamics of the kinetic temperature of a finite one-dimensional harmonic chain, the evolution of which is initiated by a thermal shock. We demonstrate that the kinetic temperature returns arbitrarily close to its initial state (the one immediately following the thermal shock) infinitely many times, and we give an estimate for the time elapsed until the recurrence. This assertion is closely related to the Poincare recurrence theorem and we discuss their relation. To estimate the recurrence time we use its averaging along system’s trajectory and provide a rigorous mathematical definition of the mean recurrence time. It turns out that the mean recurrence time exponentially increases with the number of particles in the chain. A connection is established between this problem and the local theorems of large deviations theory.

Previous studies have shown that in such a one-dimensional harmonic chain, at times of order

N

, a thermal echo phenomenon is observed — a sharp increase in the amplitude of kinetic temperature fluctuations. In the present work, we give a rigorous mathematical formulation to this phenomenon and estimate the amplitude of the fluctuations.

The research is funded by the Ministry of Science and Higher Education of the Russian Federation within the framework of the Research Center of World-Class Program: Advanced Digital Technologies (agreement №075-15-2020-311 dated 04.20.2022).

我们研究了由热冲击引发的有限一维谐波链动力学温度的演变。我们证明了动能温度会无限多次地返回到其初始状态（紧随热冲击之后的状态），并给出了直到复现所需的时间估计值。这一论断与庞加莱复现定理密切相关，我们将讨论它们之间的关系。为了估算复发时间，我们采用了沿系统轨迹平均复发时间的方法，并给出了平均复发时间的严格数学定义。结果发现，平均递推时间随链中粒子数量的增加而呈指数增长。以前的研究表明，在这样的一维谐波链中，当时间为 N 阶时，会出现热回声现象--动能温度波动幅度急剧增加。本研究由俄罗斯联邦科学和高等教育部在世界一流计划研究中心框架内资助：该研究由俄罗斯联邦科学和高等教育部在 "世界一流计划：先进数字技术 "研究中心框架内提供资助（协议编号：075-15-2020-311，日期：04.20.2022）。

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引用次数: 0

On the calibration and improvement of human mobility models in intercity transportation system 论城际交通系统中人员流动模型的校准与改进

IF 2.8 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physica A: Statistical Mechanics and its Applications

Pub Date : 2024-09-23 DOI: 10.1016/j.physa.2024.130116

Weijie Yu, Haosong Wen, Wei Wang, De Zhao, Xuedong Hua

As one of the research highlights of physics-level modelling, human mobility has generated numerous universal laws over the past decades. However, the majority of research has concentrated on the intracity networks, leaving the intercity mobility systems with insufficient attention despite its increasingly crucial role in the development of urban agglomerations. Related research gaps further extend to the limited understanding of spatiotemporal heterogeneity in intercity human mobility. To bridge these gaps, our study systematically validated and improved the modelling framework of intercity mobility flows utilizing real-world data sources. Specifically, building upon the nationwide Location-based Services (LBS) datasets in China, the applicability of classic human mobility models, including gravity model and intervening opportunities-class models, was extensively explored in the intercity domain by developing fitting models that incorporated multi-class urban attributes. Then, we contributed to proposing improved models that consider the diverse attraction effect of the origin and potential destinations. Moreover, our research scope was expanded to incorporate spatiotemporal heterogeneity through model comparisons among various city sets during both regular period and holiday. The findings suggested that our improved models effectively enhance the modelling accuracy while strengthening the explanatory power. They especially demonstrate a balanced performance even when handling datasets with spatiotemporal heterogeneity. Consequently, this study provides valuable insights into understanding intercity human mobility from the intrinsic mechanism of opportunity attraction. Our models hold practical significance in accurately modelling intercity mobility flows utilizing observable urban attributes and spatial layouts, further providing effective tools for preemptive traffic management.

作为物理学建模的研究重点之一，人类流动性在过去几十年中产生了许多普遍规律。然而，大多数研究都集中在城内网络上，对城际流动系统的关注不够，尽管它在城市群的发展中扮演着越来越重要的角色。相关的研究空白进一步扩展到对城际间人员流动的时空异质性的有限理解。为了弥补这些差距，我们的研究利用现实世界的数据来源，系统地验证并改进了城际流动的建模框架。具体而言，我们以中国全国范围内的位置服务（LBS）数据集为基础，通过开发包含多类城市属性的拟合模型，广泛探讨了重力模型和干预机会类模型等经典人员流动模型在城际领域的适用性。随后，我们提出了考虑出发地和潜在目的地不同吸引效应的改进模型。此外，我们还扩大了研究范围，通过在平时和节假日期间对不同城市集进行模型比较，纳入了时空异质性。研究结果表明，我们改进的模型有效地提高了建模精度，同时增强了解释力。尤其是在处理具有时空异质性的数据集时，这些模型表现出了均衡的性能。因此，本研究为从机会吸引的内在机制来理解城市间人口流动提供了宝贵的见解。我们的模型在利用可观测的城市属性和空间布局对城际流动进行精确建模方面具有重要的现实意义，并进一步为先发制人的交通管理提供了有效工具。

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引用次数: 0

Cellular automaton model for the analysis of design and plan of bus station in the mixed traffic environment 用于分析混合交通环境下公交车站设计和规划的细胞自动机模型

IF 2.8 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physica A: Statistical Mechanics and its Applications

Pub Date : 2024-09-20 DOI: 10.1016/j.physa.2024.130106

Jiemin Xie , Mengqi Chen , Linlin You , Gege Jiang , Junxian Wu , Tuo Sun , Ruochen Hao

With the quick development of Connected Autonomous Vehicles (CAVs), CAVs would gradually become an important part of urban traffic. Hence, the impacts of CAVs on urban traffic should be further explored. This study aims to analyze the mixed traffic comprising CAVs and human-driven vehicles (HDVs) in different urban scenarios in which different bus station types (i.e., roadside and bay bus stations) and capacities are considered. To do this analysis, this study proposes a cellular automaton model which simulates car following behaviours of vehicles using a two-state safe speed model, and designs specific modeling rules for lane-changing behaviours and vehicle behaviours near bus stations with consideration of the differences between CAVs and HDVs. The analysis results indicate that the impacts of various bus station types and capacities on the mixed traffic flow vary with traffic volumes, while increasing the CAV penetration rate can reduce the traffic congestion caused by bus stop-and-go. Furthermore, the study explores the optimal number of bus routes for different types of bus stations in different urban traffic scenarios, and several possible policy implications have been given according to the analysis results.

随着车联网自动驾驶汽车（CAV）的快速发展，CAV 将逐渐成为城市交通的重要组成部分。因此，应进一步探讨 CAV 对城市交通的影响。本研究旨在分析不同城市场景下由 CAV 和人类驾驶车辆（HDV）组成的混合交通，其中考虑了不同的公交车站类型（即路边公交车站和港湾式公交车站）和容量。为进行上述分析，本研究提出了一种蜂窝自动机模型，该模型利用双态安全速度模型模拟车辆的跟车行为，并考虑到 CAV 和 HDV 的差异，为公交车站附近的变道行为和车辆行为设计了特定的建模规则。分析结果表明，各种公交车站类型和容量对混合交通流的影响随交通流量的变化而变化，而提高 CAV 的渗透率可以减少公交车走走停停造成的交通拥堵。此外，研究还探讨了不同类型公交站点在不同城市交通情景下的最佳公交线路数量，并根据分析结果给出了几种可能的政策含义。

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引用次数: 0

Effects of uncertain anomalous information on traffic flow of automated vehicles with V2V communication 不确定异常信息对带有 V2V 通信功能的自动驾驶汽车交通流的影响

IF 2.8 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physica A: Statistical Mechanics and its Applications

Pub Date : 2024-09-19 DOI: 10.1016/j.physa.2024.130107

Shihao Li , Bojian Zhou , Ting Wang , Cheng Cheng , Min Xu

Automated vehicles (AVs) equipped with vehicle-to-vehicle (V2V) communication can operate by sensing real-time status information through onboard sensors and wireless connections. Nevertheless, under the influence of multifarious random factors in real traffic, this critical information that support the normal movement of such vehicles may be anomalous, raising concerns on their mobility and traffic security. Due to the lack of appropriate analytical model, previous studies have not comprehensively uncovered the effects of uncertain anomalous information on traffic flow of AVs with V2V communication. Therefore, this study aims to bridge this critical gap. Firstly, by introducing a probabilistic parameter (i.e., information anomaly probability), we propose a general model that integrates the normal and compromised models, thereby capturing the longitudinal dynamics of AVs featuring V2V communication in the presence of uncertain anomalous information. To enable the detailed theoretical and experimental analyses, we specify it through the cooperative adaptive cruise control model calibrated with real-car data. Subsequently, we define the concept of pseudo string stability and parameterize the stability condition based on the characteristic equation method, so as to demonstrate the relationship between traffic flow stability and the parameters and probability of information anomaly. Finally, we refine the proposed probabilistic model and conduct extensive numerical experiments. The findings show that uncertain anomalous information could result in sudden or even frequent acceleration and deceleration of AVs, causing traffic oscillation, reduced traffic efficiency, and even collision accidents. In particular, the greater the information anomaly probability, the larger the disturbances experienced by traffic flow. Meanwhile, at the same level of anomaly, the combined impacts of various anomalous information could lead to more severe consequences than the singular impact of any individual anomalous information. Furthermore, the duration of anomalous information directly affects the time it takes for traffic flow to return to normal.

配备了车对车（V2V）通信功能的自动驾驶汽车（AV）可以通过车载传感器和无线连接感知实时状态信息。然而，在现实交通中各种随机因素的影响下，这些支持车辆正常行驶的关键信息可能会出现异常，从而引发对其机动性和交通安全的担忧。由于缺乏适当的分析模型，以往的研究没有全面揭示不确定的异常信息对具有 V2V 通信功能的自动驾驶汽车交通流的影响。因此，本研究旨在填补这一关键空白。首先，通过引入一个概率参数（即信息异常概率），我们提出了一个整合了正常模型和妥协模型的通用模型，从而捕捉到了具有 V2V 通信功能的自动驾驶汽车在不确定异常信息下的纵向动态。为了进行详细的理论和实验分析，我们通过使用实车数据校准的合作式自适应巡航控制模型来具体说明该模型。随后，我们定义了伪串稳定性的概念，并基于特征方程法对稳定性条件进行了参数化，从而证明了交通流稳定性与信息异常参数和概率之间的关系。最后，我们完善了所提出的概率模型，并进行了大量的数值实验。研究结果表明，不确定的异常信息会导致自动驾驶汽车突然甚至频繁地加速和减速，造成交通振荡，降低交通效率，甚至引发碰撞事故。特别是，信息异常概率越大，交通流受到的干扰就越大。同时，在相同的异常水平下，各种异常信息的综合影响可能比任何单个异常信息的单一影响导致更严重的后果。此外，异常信息的持续时间会直接影响交通流恢复正常所需的时间。

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引用次数: 0

Assortativity in sympatric speciation and species classification 同域物种变异和物种分类中的同源性

IF 2.8 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physica A: Statistical Mechanics and its Applications

Pub Date : 2024-09-19 DOI: 10.1016/j.physa.2024.130111

Joao U.F. Lizárraga , Flavia M.D. Marquitti , Marcus A.M. de Aguiar

We investigate the role of assortative mating in speciation using the sympatric model of Derrida and Higgs. The model explores the idea that genetic differences create incompatibilities between individuals, preventing mating if the number of such differences is too large. Speciation, however, only happens in this mating system if the number of genes is large. Here we show that speciation with small genome sizes can occur if assortative mating is introduced. In our model individuals are represented by three chromosomes: one responsible for reproductive compatibility, one for coding the trait on which assortativity will operate, and a neutral chromosome. Reproduction is possible if individuals are genetically similar with respect to the first chromosome, but among these compatible mating partners, the one with the most similar trait coded by the second chromosome is selected. We show that this type of assortativity facilitates speciation, which can happen with a small number of genes in the first chromosome. Species, classified according to reproductive isolation, dictated by the first chromosome, can display different traits values, as measured by the second and the third chromosomes. Therefore, species can also be identified based on similarity of the neutral trait, which works as a proxy for reproductive isolation.

我们利用德里达（Derrida）和希格斯（Higgs）的同种交配模型研究了同种交配在物种分化中的作用。该模型探讨的观点是，基因差异会造成个体间的不相容性，如果这种差异数量过大，就会阻碍交配。然而，在这种交配系统中，只有当基因数量很大时，物种才会发生分化。在这里，我们证明，如果引入同配交配，基因组规模较小的物种也会出现。在我们的模型中，个体由三条染色体代表：一条负责生殖兼容性，一条负责编码同配性状，还有一条中性染色体。如果个体与第一条染色体的基因相似，那么就可以进行繁殖，但在这些相容的交配对象中，由第二条染色体编码的性状最相似的个体会被选中。我们的研究表明，这种类型的同配性有利于物种的形成，而第一条染色体上的基因数量较少就能实现物种的形成。根据第一条染色体所决定的生殖隔离进行分类的物种，可以显示出第二和第三条染色体所衡量的不同性状值。因此，也可以根据中性性状的相似性来识别物种，中性性状可以作为生殖隔离的替代物。

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引用次数: 0

Emissions-reduction strategy for connected autonomous vehicles on mixed traffic freeways 互联自动驾驶汽车在混合交通高速公路上的减排策略

IF 2.8 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physica A: Statistical Mechanics and its Applications

Pub Date : 2024-09-19 DOI: 10.1016/j.physa.2024.130113

Yanyan Qin , Tengfei Xiao , Zhengbing He

Acceleration and deceleration behaviors negatively affect car-following dynamics of vehicles on freeways, leading to traffic oscillations, thus increasing transportation emissions. The emergence of connected autonomous vehicles (CAVs) offers a potential to mitigate these effects. This paper aims to propose a car-following strategy for CAVs to reduce transportation emissions on mixed traffic freeways. Firstly, we adopted the calibrated Gipps model to characterize car-following behaviors of human-driven vehicles (HDVs). Based on this, we proposed a car-following strategy for CAVs designed to mitigate traffic oscillations and reduce transportation emissions. Subsequently, we introduced a simulation framework for analyzing transportation emissions. Finally, considering foggy weather as a practical application, we validated the effectiveness of our proposed CAV car-following strategy, by evaluating transportation emissions under different conditions, including three emission categories, varying CAV market presentation rates (MPRs), two foggy levels, and four speed limits. The results show a close correlation between transportation emissions and traffic oscillations, indicating that increased oscillations result in higher emissions. The proposed CAV strategy demonstrates significant efficacy in mitigating traffic oscillations and reducing transportation emissions in foggy weather. As the MPR of CAVs equipped with our strategy increases, transportation emissions decrease gradually. Specifically, at an MPR of 1, the average reductions in CO, HC, and NO_x emissions reach 16.99 %, 11.65 %, and 20.82 %, respectively. Following findings from our analysis, recommended insights are provided for speed limit strategy and CAV dedicated lane management for mixed traffic on foggy freeways, from the perspective of reducing emissions.

加速和减速行为会对高速公路上车辆的跟车动态产生负面影响，导致交通振荡，从而增加交通排放。联网自动驾驶汽车（CAV）的出现为减轻这些影响提供了可能。本文旨在提出一种 CAV 的跟车策略，以减少混合交通高速公路上的交通排放。首先，我们采用经过校准的 Gipps 模型来描述人类驾驶车辆（HDV）的跟车行为。在此基础上，我们提出了旨在缓解交通振荡和减少交通排放的 CAV 跟车策略。随后，我们介绍了分析交通排放的模拟框架。最后，考虑到大雾天气的实际应用，我们通过评估不同条件下的交通排放，包括三种排放类别、不同的 CAV 市场展示率（MPR）、两种雾度和四种速度限制，验证了我们提出的 CAV 汽车跟随策略的有效性。结果显示，交通排放与交通振荡密切相关，表明振荡增加会导致排放增加。所提出的 CAV 策略在缓解交通振荡和减少雾天交通排放方面效果显著。随着采用我们策略的 CAV 的 MPR 增加，交通排放也逐渐减少。具体而言，当 MPR 为 1 时，一氧化碳、碳氢化合物和氮氧化物的平均排放量分别减少了 16.99%、11.65% 和 20.82%。根据我们的分析结果，从减少排放的角度出发，为雾天高速公路混合交通的限速策略和 CAV 专用车道管理提供了建议性意见。

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引用次数: 0

Flux-quench induced dynamical quantum phase transitions in an extended XY spin-chain 扩展 XY 自旋链中通量淬火诱导的动态量子相变

IF 2.8 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physica A: Statistical Mechanics and its Applications

Pub Date : 2024-09-18 DOI: 10.1016/j.physa.2024.130110

Wen-Hui Nie, Mei-Yu Zhang, Lin-Cheng Wang

Dynamical quantum phase transitions (DQPTs) induced by flux-quench in an extended transversed XY spin-chain have been investigated in this paper. We discussed the conditions for the appearance of DQPTs, and the different regions of the flux quench restricted by strength of transverse field were given. The Loschmidt echo, rate function, geometric phase, as well as dynamical topological order parameter (DTOP) have been calculated, which consistently verified the emergence of DQPTs.

本文研究了在扩展的横向 XY 自旋链中由通量淬火诱发的动态量子相变（DQPTs）。我们讨论了 DQPTs 出现的条件，并给出了受横向场强限制的不同通量淬火区域。我们计算了洛希米特回波、速率函数、几何相位以及动力学拓扑阶次参数（DTOP），结果一致验证了 DQPT 的出现。

引用次数: 0

Controllability of higher-order networks 高阶网络的可控性

IF 2.8 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physica A: Statistical Mechanics and its Applications

Pub Date : 2024-09-17 DOI: 10.1016/j.physa.2024.130108

Weiyuan Ma, Xionggai Bao, Chenjun Ma

Higher-order networks can comprehensively describe interactions among groups, thus emerging as a novel area of exploration in network science. This paper aims to delve into the controllability of higher-order networks, where the network topology is characterized by higher-order interactions and the nodes are higher-dimensional dynamical systems. The collective effects on the network controllability from the dynamics of higher-order interactions, node dynamics, inner interactions, and external control inputs are extensively explored. By applying matrix theory and control theory, some necessary and/or sufficient conditions are developed to determine the controllability of hypergraph networks and simplicial complex networks. Through simulated examples, it becomes evident that the controllability of higher-order networked system is far more complicated than that of traditional networked systems and the higher-order topological structures facilitate the controllability. Remarkably, the integrated network can achieve controllability even when the corresponding traditional network is uncontrollable by external inputs.

高阶网络可以全面描述群体间的相互作用，因此成为网络科学的一个新的探索领域。本文旨在深入研究高阶网络的可控性。高阶网络的拓扑特征是高阶交互，节点是高维动态系统。本文广泛探讨了高阶交互动态、节点动态、内部交互和外部控制输入对网络可控性的集体影响。通过应用矩阵理论和控制理论，提出了确定超图网络和简单复杂网络可控性的一些必要和/或充分条件。通过模拟实例，可以明显看出高阶网络系统的可控性比传统网络系统复杂得多，而高阶拓扑结构有助于提高可控性。值得注意的是，即使相应的传统网络无法控制外部输入，集成网络也能实现可控性。

引用次数: 0