Networks Of Dynamical Systems Research Articles

Event-triggered H∞ control for networked dynamic system with nonideal interconnection

This paper studies the event-triggered H∞ control problem of the networked dynamic system composed of heterogeneous subsystems with nonideal interconnection. Firstly, the considered system is transformed into a time-delay system of high dimension on the basis of well-posedness. Then, a lemma is derived by constructing a sampled-data-dependent Lyapunov functional to ensure the stability with a given H∞ performance of the time-delay system. Next, by fully using the information of the interconnected structure, sufficient conditions that only involve individual subsystem's parameters are established to guarantee the well-posedness, stability and H∞ performance of the controlled networked dynamic system. Based on these conditions, the simultaneous design for the controller gain and the trigger weight matrix is achieved. Finally, the effectiveness of the obtained co-design method is certified by two examples.

The recoverability of network controllability with respect to node additions

Network controllability is a critical attribute of dynamic networked systems. Investigating methods to restore network controllability after network degradation is crucial for enhancing system resilience. In this study, we develop an analytical method based on degree distributions to estimate the minimum fraction of required driver nodes for network controllability under random node additions after the random removal of a subset of nodes. The outcomes of our method closely align with numerical simulation results for both synthetic and real-world networks. Additionally, we compare the efficacy of various node recovery strategies across directed Erdös–Rényi (ER) networks, swarm signaling networks (SSNs), and directed Barabàsi Albert (BA) networks. Our findings indicate that the most efficient recovery strategy for directed ER networks and SSNs is the greedy strategy, which considers node betweenness centrality. Similarly, for directed BA networks, the greedy strategy focusing on node degree centrality emerges as the most efficient. These strategies outperform recovery approaches based on degree centrality or betweenness centrality, as well as the strategy involving random node additions.

Localized and Incremental Probabilistic Inference for Large-Scale Networked Dynamical Systems

Localized and Incremental Probabilistic Inference for Large-Scale Networked Dynamical Systems

Dynamic Neural Network for Bicriteria Weighted Control of Robot Manipulators.

In recent years, bicriteria optimization schemes for manipulator control have become preferred by researchers, given their satisfactory performance. In this article, a bicriteria weighted (BCW) scheme to remedy joint drift and minimize the infinity norm of joint velocity is proposed. The scheme adopts a novel repetitive motion index that can theoretically decouple the joint error and the position error, which many conventional cyclic motion generation schemes cannot achieve. Subsequently, through transformation, the BCW scheme is converted into a time-varying quadratic programming (QP) problem. Then, a dynamic neural network (DNN) system with a new Fisher-Burmeister function is proposed to address the resulting QP problem. It is proven that the proposed DNN system is free of residual errors, which means that the actual solution is able to converge to the theoretical solution. Another essential feature of the DNN system is that it has a suppression effect on noise. To demonstrate the convergence and robustness of the proposed DNN system, comparative simulations are carried out in nominal and noisy environments. Finally, experiments on Franka Emika Panda are conducted to elucidate the availability of the BCW scheme addressed by the DNN system.

Network dynamics with higher-order interactions: coupled cell hypernetworks for identical cells and synchrony

Network interactions that are nonlinear in the state of more than two nodes—also known as higher-order interactions—can have a profound impact on the collective network dynamics. Here we develop a coupled cell hypernetwork formalism to elucidate the existence and stability of (cluster) synchronization patterns in network dynamical systems with higher-order interactions. More specifically, we define robust synchrony subspace for coupled cell hypernetworks whose coupling structure is determined by an underlying hypergraph and describe those spaces for general such hypernetworks. Since a hypergraph can be equivalently represented as a bipartite graph between its nodes and hyperedges, we relate the synchrony subspaces of a hypernetwork to balanced colourings of the corresponding incidence digraph.

Network centrality, support organizations, exploratory innovation: Empirical analysis of China's integrated circuit industry

Exploratory innovation is critical to the breakthrough of core technologies in the integrated circuit (IC) industry, and cooperative innovation is a promising form of IC industry development. According to the viewpoint of social network, this paper constructs intercity networks of the IC industry by using a data set of cooperation patents from 2011 to 2020 in China. We uncover the evolution characteristics of the innovation networks, explore the relationship between network centrality and exploratory innovation in a city, and consider universities and development zones, named support organizations, as moderating variables. The results of the social network analysis (SNA) and dynamic panel system generalized method of moments model (System-GMM) are given as follows: Cities are increasingly inclined to collaborate with counterparts over time for innovation, but the overall network scale remains small. Beijing occupies core position in the networks. A cooperative innovation model driven by peripheral cities has been formed as the number of the peripheral cities has gradually increased. The network centrality of a city has a positive effect on its exploratory innovation. Both universities and development zones positively moderate the effect of network centrality on exploratory innovation. Based on the characteristics of the network, our study reveals the importance of taking the internal structure of the network and the node support environment into the same framework, which provides guidance for the innovative development of the world IC industry.

Recovering the Graph Underlying Networked Dynamical Systems under Partial Observability: A Deep Learning Approach

We study the problem of graph structure identification, i.e., of recovering the graph of dependencies among time series. We model these time series data as components of the state of linear stochastic networked dynamical systems. We assume partial observability, where the state evolution of only a subset of nodes comprising the network is observed. We propose a new feature-based paradigm: to each pair of nodes, we compute a feature vector from the observed time series. We prove that these features are linearly separable, i.e., there exists a hyperplane that separates the cluster of features associated with connected pairs of nodes from those of disconnected pairs. This renders the features amenable to train a variety of classifiers to perform causal inference. In particular, we use these features to train Convolutional Neural Networks (CNNs). The resulting causal inference mechanism outperforms state-of-the-art counterparts w.r.t. sample-complexity. The trained CNNs generalize well over structurally distinct networks (dense or sparse) and noise-level profiles. Remarkably, they also generalize well to real-world networks while trained over a synthetic network -- namely, a particular realization of a random graph.

Transitions between peace and systemic war as bifurcations in a signed network dynamical system

AbstractWe investigate structural features and processes associated with the onset of systemic conflict using an approach which integrates complex systems theory with network modeling and analysis. We present a signed network model of cooperation and conflict dynamics in the context of international relations between states. The model evolves ties between nodes under the influence of a structural balance force and a dyad-specific force. Model simulations exhibit a sharp bifurcation from peace to systemic war as structural balance pressures increase, a bistable regime in which both peace and war stable equilibria exist, and a hysteretic reverse bifurcation from war to peace. We show how the analytical expression we derive for the peace-to-war bifurcation condition implies that polarized network structure increases susceptibility to systemic war. We develop a framework for identifying patterns of relationship perturbations that are most destabilizing and apply it to the network of European great powers before World War I. We also show that the model exhibits critical slowing down, in which perturbations to the peace equilibrium take longer to decay as the system draws closer to the bifurcation. We discuss how our results relate to international relations theories on the causes and catalysts of systemic war.

Dynamic management network system of automobile detection applying edge computing

AbstractDynamic vehicle detection requires the transmission of large amounts of data collected by different types of sensors to the edge computing nodes. This is likely to cause network delays and congestion, affecting the computation of the edge computing nodes and thus posing serious security risks. Therefore, optimizing data transmission between vehicles and edge computing nodes is a new challenge to be addressed in the practical application of edge computing‐based vehicle dynamic detection architectures. The data requirements of VDT for vehicle detection dynamic detection in different environments are considered, the optimization objectives and constraints are analysed, and a deviation detection and greedy algorithm is proposed in this paper to address the problems of long mixed‐integer linear programme solution time and insufficient practical applications, and the performance of the algorithm is evaluated through simulation experiments conducted by simulation of urban mobility, a traffic flow simulation tool, and PreScan, a vehicle simulation test software. The results show that compared with the deviation detection algorithm, the greedy algorithm can reduce the communication overhead by 82.6%–86.2% in all cases and improve the performance by 13.6%–19.5%, which is more suitable for practical applications. The results of this paper contribute to the automation and modernization of vehicle technology management and information transfer.

On quantification and maximization of information transfer in network dynamical systems

Information flow among nodes in a complex network describes the overall cause-effect relationships among the nodes and provides a better understanding of the contributions of these nodes individually or collectively towards the underlying network dynamics. Variations in network topologies result in varying information flows among nodes. We integrate theories from information science with control network theory into a framework that enables us to quantify and control the information flows among the nodes in a complex network. The framework explicates the relationships between the network topology and the functional patterns, such as the information transfers in biological networks, information rerouting in sensor nodes, and influence patterns in social networks. We show that by designing or re-configuring the network topology, we can optimize the information transfer function between two chosen nodes. As a proof of concept, we apply our proposed methods in the context of brain networks, where we reconfigure neural circuits to optimize excitation levels among the excitatory neurons.

Improving Continuous Hopfield Network Stability Using Runge-Kutta Method

Continuous Hopfield network is a recurring network that has shown its ability to solve important optimization problems. Continuous Hopfield network dynamic system is characterized by a differential equation. This equation is difficult to solve, especially for large problems. This led researchers to discretize the differential equation using Euler’s method. However, this method generally does not converge to a good solution because it is sensitive to the step size decision and initial conditions. In this work, we discretize the dynamic system of continuous Hopfield network by a new method of Runge-Kutta. This method is strong in terms of stability and performance in order to converge to a better solution. This new method introduces two phases for better network stability. The first phase targets to solve the dynamic equation by the Euler method, while the second phase allows refining the solution found in the first phase. Experimental results on benchmarks show that the proposed approach can effectively improve Hopfield neural network performance.

Social Depolarization and Diversity of Opinions-Unified ABM Framework.

Most sociophysics opinion dynamics simulations assume that contacts between agents lead to greater similarity of opinions, and that there is a tendency for agents having similar opinions to group together. These mechanisms result, in many types of models, in significant polarization, understood as separation between groups of agents having conflicting opinions. The addition of inflexible agents (zealots) or mechanisms, which drive conflicting opinions even further apart, only exacerbates these polarizing processes. Using a universal mathematical framework, formulated in the language of utility functions, we present novel simulation results. They combine polarizing tendencies with mechanisms potentially favoring diverse, non-polarized environments. The simulations are aimed at answering the following question: How can non-polarized systems exist in stable configurations? The framework enables easy introduction, and study, of the effects of external "pro-diversity", and its contribution to the utility function. Specific examples presented in this paper include an extension of the classic square geometry Ising-like model, in which agents modify their opinions, and a dynamic scale-free network system with two different mechanisms promoting local diversity, where agents modify the structure of the connecting network while keeping their opinions stable. Despite the differences between these models, they show fundamental similarities in results in terms of the existence of low temperature, stable, locally and globally diverse states, i.e., states in which agents with differing opinions remain closely linked. While these results do not answer the socially relevant question of how to combat the growing polarization observed in many modern democratic societies, they open a path towards modeling polarization diminishing activities. These, in turn, could act as guidance for implementing actual depolarization social strategies.

Reinforcement Learning of Structured Stabilizing Control for Linear Systems With Unknown State Matrix

This article delves into designing stabilizing feedback control gains for continuous-time linear systems with unknown state matrix, in which the control gain is subjected to a structural constraint. We bring forth the ideas from reinforcement learning (RL) in conjunction with sufficient stability and performance guarantees in order to design these structured gains using the trajectory measurements of states and controls. We first formulate a model-based linear quadratic regulator (LQR) framework to compute the structured control gain. Subsequently, we transform this model-based LQR formulation into a data-driven RL algorithm to remove the need for knowing the system state matrix. Theoretical guarantees are provided for the stability of the closed-loop system and the convergence of the structured RL (SRL) algorithm. A remarkable application of the proposed SRL framework is in designing distributed static feedback control, which is necessary for automatic control of many large-scale cyber–physical systems. As such, we validate our theoretical results with numerical simulations on a multiagent networked linear time-invariant dynamical system.

Bounded Partial Pinning Control of Network Dynamical Systems

Controlling collective behavior has been the key goal of researchers both from the engineering and physics communities working in the field of control of network systems. In the literature, pinning control has often emerged as the tool of choice to achieve this task. Only recently, though, has the problem of controlling only a fraction of the network nodes been tackled. Here, we consider the case in which, due to the disturbing influence of an external node, which we identify as an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opponent</i> , the network nodes cannot asymptotically converge to the pinner's trajectory, and only a bounded convergence can be achieved. We derive analytic conditions guaranteeing that all the nodes in a given strongly connected component of the network achieve bounded convergence to the trajectory of the pinner, and provide an estimate of the convergence bound. Finally, we apply our results to an opinion dynamics scenario, showing that a pinned node selection strategy grounded on our theoretical results is effective in steering the opinions of the majority of the network nodes toward that of the pinner.

Structural inference of networked dynamical systems with universal differential equations.

Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical) units to exhibit a wide range of nontrivial behaviors, such as the emergence of coherent structures (e.g., waves and patterns) or otherwise notable dynamics (e.g., synchrony and chaos). In this work, we seek to infer (i) the intrinsic physics of a base unit of a population, (ii) the underlying graphical structure shared between units, and (iii) the coupling physics of a given networked dynamical system given observations of nodal states. These tasks are formulated around the notion of the Universal Differential Equation, whereby unknown dynamical systems can be approximated with neural networks, mathematical terms known a priori (albeit with unknown parameterizations), or combinations of the two. We demonstrate the value of these inference tasks by investigating not only future state predictions but also the inference of system behavior on varied network topologies. The effectiveness and utility of these methods are shown with their application to canonical networked nonlinear coupled oscillators.

Direct Data Driven Control for UAVs Formation Dynamic Network

This new paper applies the novel direct data driven control into UAVs formation dynamic network and designs the distributed controller for each UAV, while guaranteeing the desired flight performance. Firstly, a new control architecture is constructed as an unified framework for UAV task implementation, including the management layer, functional layer and physical layer together. Secondly, we explain one special dynamic network,i.e. network modules, exist in above control architecture, and the process about how to operate these network modules in described in detail. Thirdly, after introducing the idea of distributed control and the dynamic network system, our main contribution concern on how to apply direct data driven control to design these distributed controllers for all UAVs respectively. Furthermore, the detailed derivations and one improvement are combined to complete our own proposed theoretical results. Finally, one simulation example confirms above theories.

Computer virus propagation models: A mathematical review

The physical world has come together by the connection of devices on an extra ordinary level through internet of things. This forms a very complex and dynamic network system and number of heterogeneous device are connected with each other. Physical objects connected in a network, interchange data with other connected devices via communication networks. The data interchange is very helpful in a number of domains in day-to-day life of human beings. Security of connection and data is one of the major challenges for this connection and communication. A computer virus is a potential threat resulting into the damage of connected devices into a network and the data. Epidemic models, similar with biological virus spread models, are widely studied to investigate the behaviour of computer viruses. The primary objective of the article is to categorize a number of computer virus propagation model, so that their comparative studies becomes easier. This article contains a qualitative review and categorization of computer virus propagation models into three categories, namely, compartment model, network model and stochastic model. The study is helpful to further investigate the virus propagation mechanism and to control them optimally.

Detection of Delays and Feedthroughs in Dynamic Networked Systems

This letter presents systematic tests to determine if a particular transfer function in an interconnected system is strictly proper or has a feedthrough. Considering a strictly proper module between two nodes in a networked system, if only the data of the two nodes are used, there are situations where numerical tests to determine if the module is strictly proper will fail. It is shown, however, that marginalizing some of the nodes of a networked system under certain conditions preserves delays and feedthroughs in certain links. Therefore, using a set of auxiliary nodes that satisfies certain conditions, it is possible to design a systematic test to determine if a module in the networked system is strictly proper. The conditions are proven to be sufficient. Similar ideas are used to formulate a systematic test to determine if a module has a feedthrough.

Special Issue on: Advancements in Mathematics and Optimization Techniques in Technology &amp; Business

Advancements in Mathematics and Optimization Techniques in Technology and Business are integral components of numerous scientific and practical domains, providing valuable tools for understanding complex phenomena, making informed decisions, and predicting outcomes. Over the years, these disciplines have witnessed significant advancements, driven by the relentless pursuit of improved methodologies, the availability of vast amount of data, and the need to address increasingly intricate real-world problems. One of the key areas of focus in this special issue is the development of mathematical modeling techniques for complex systems which are characterized by their intricate interconnectedness, making them challenging to study and analyze. Researchers have made significant strides in developing sophisticated mathematical models and computational methods to simulate and understand such systems. Network modeling, agent-based modeling, stochastic modeling, and dynamical systems are among the areas that have seen remarkable progress, enabling researchers to gain deeper insights into the behavior and dynamics of complex systems.

Competitive Epidemic Spreading Over Networks

In this letter, we consider an epidemic model for two competitive viruses spreading over a metapopulation network, termed the ‘bivirus model’ for convenience. The dynamics are described by a networked continuous-time dynamical system, with each node representing a population and edges representing infection pathways for the viruses. We survey existing results on the bivirus model beginning with the nature of the equilibria, including whether they are isolated, and where they exist within the state space with the corresponding interpretation in the context of epidemics. We identify key convergence results, including the conclusion that for generic system parameters, global convergence occurs for almost all initial conditions. Conditions relating to the stability properties of various equilibria are also presented. In presenting these results, we also recall some of the key tools and theories used to secure them. We conclude by discussing the various open problems, ranging from control and network optimization, to further characterization of equilibria, and finally extensions such as modeling three or more viruses.