Networks Of Dynamical Systems Research Articles

Identifying edges that facilitate the generation of extreme events in networked dynamical systems.

The collective dynamics of complex networks of FitzHugh-Nagumo units exhibits rare and recurrent events of high amplitude (extreme events) that are preceded by so-called proto-events during which a certain fraction of the units become excited. Although it is well known that a sufficiently large fraction of excited units is required to turn a proto-event into an extreme event, it is not yet clear how the other units are being recruited into the final generation of an extreme event. Addressing this question and mimicking typical experimental situations, we investigate the centrality of edges in time-dependent interaction networks. We derived these networks from time series of the units' dynamics employing a widely used bivariate analysis technique. Using our recently proposed edge-centrality concepts together with an edge-based network decomposition technique, we observe that the recruitment is primarily facilitated by sets of certain edges that have no equivalent in the underlying topology. Our finding might aid to improve the understanding of generation of extreme events in natural networked dynamical systems.

The Effect of Shadow Banking on the Systemic Risk in a Dynamic Complex Interbank Network System

After the financial crisis triggered by the subprime mortgage crisis in the United States in 2008, many scholars believed that the unstable transmission of shadow banking business in the banking system is the main factor causing financial turmoil. This paper proposes a dynamic complex interbank network system model with shadow banking in which the dynamic complex interbank network system differs from the traditional banking network and is formed by the interrelated business between shadow banks and commercial banks to explore the effect of shadow banking on the systemic risk. The results show that the existence of shadow banking will increase the systemic risk, accelerate the speed of bankruptcy of banks, reduce the survival ratio of banks, and increase the strength of central bank assistance. The smaller the number of shadow banks in the system, the higher the degree of credit connection among commercial banks and the smaller the systemic risk.

Mean field dynamics of stochastic cellular automata for random and small-world graphs

We aim to provide a theoretical framework to explain the discrete transitions of mood connecting ideas from network theory and dynamical systems theory. It was recently shown how networks (graphs) can be used to represent psychopathologies, where symptoms of, say, depression, affect each other and certain configurations determine whether someone could transition into a depression. To analyse changes over time and characterise possible future behaviour is in general rather difficult for large graphs. We describe the dynamics of graphs using one-dimensional discrete time dynamical systems theory obtained from a mean field approximation to stochastic cellular automata (SCA). Often the mean field approximation is used on a regular graph (a grid or torus) where each node has the same number of edges and the same probability of becoming active. We provide quantitative results on the accuracy of using the mean field approximation for the grid and random and small-world graph to describe the dynamics of the SCA. Bifurcation diagrams for the mean field of the different graphs indicate possible phase transitions for certain parameter settings of the mean field. Simulations confirm for different graph sizes (number of nodes) that the mean field approximation is accurate.

Discrete-Time Networked Dynamic Systems

In this paper, we provides a general framework for the analysis of a class of linear discrete-time networked dynamic systems (DNDS). We focus our attention on DNDS where the underlying connection topology couples the agents at their outputs. A distinction is made between DNDS with homogeneous agent dynamics and DNDS with heterogeneous agent dynamics. It is emphasized that developing efficient solution methods for the design of such systems involve connecting and interpreting results from graph theory and convex optimization in a systems-theoretic context

Commentary: A network science summer course for high-school students

AbstractWe discuss a two-week summer course on “Network Science” and “Complex Systems” that we taught for 15 German high-school pupils of ages 16–18. In this course, we covered topics in graph theory, applied network science, programming, and dynamic systems alike. We find that “Network Science” is a well-suited course for introducing students to university-level mathematics. We reflect on difficulties regarding programming exercises and the discussion of more advanced topics in dynamic systems. We make the course material available and encourage fellow network scientists to organize similar outreach events.

Network dynamic defense system based on holographic transformation

Aimed at the problem of the boundary defense easily being out of availability caused by the static network structure, a novel dynamic enterprise network defense system based on holographic transformation is designed and implemented. To increase the uncertainty of network structure and the position of target nodes, the network view is dynamically changed by constantly transforming endpoint information. Virtual endpoint mutation and hopping period selection are achieved by the hopping address generation module. It takes the advantages of anti-collision and good randomicity of the Chinese national SM3 hash algorithm. The full-cycle hopping period is managed and controlled by the hopping period management mechanism based on the ciphertext policy attribute-based broadcast holographic transformation. Experiments show that the system achieves expected security goals and has good interactivity and high stability.

Validity and Limitations of the Detection Matrix to Determine Hidden Units and Network Size from Perceptible Dynamics.

Determining the size of a network dynamical system from the time series of some accessible units is a critical problem in network science. Recent work by Haehne etal. [Phys. Rev. Lett. 122, 158301 (2019).PRLTAO0031-900710.1103/PhysRevLett.122.158301] has presented a model-free approach to address this problem, by studying the rank of a detection matrix that collates sampled time series of perceptible nodes from independent experiments. Here, we unveil a profound connection between the rank of the detection matrix and the control-theoretic notion of observability, upon which we conclude when and how it is feasible to exactly infer the size of a network dynamical system.

Characterizations, iterative method, sign pattern and perturbation analysis for the DMP inverse with its applications

This paper is a study on main properties and characterizations of the DMP inverse. Also, corresponding representations and computational procedures are derived. Particularly, an upgrade of the bordering method to the case of the DMP inverse is considered as well as applications of the DMP inverse in solving singular linear systems. Also, the DMP inverse of an upper block triangular matrix and its sign pattern are investigated. Furthermore, several computational procedures aimed to approximating the DMP inverse are developed, implemented and tested. The main of them are the limit representation, a revised successive matrix squaring iterations and the Gradient Neural Network (GNN) dynamical system. Finally, some perturbation bounds and continuity of the DMP inverse are studied.

Brain Network Dynamics Correlate with Personality Traits.

Identifying the neural substrates underlying the personality traits is a topic of great interest. On the other hand, it is now established that the brain is a dynamic networked system that can be studied by using functional connectivity techniques. However, much of the current understanding of personality-related differences in functional connectivity has been obtained through the stationary analysis, which does not capture the complex dynamical properties of brain networks. In this study, we aimed at evaluating the feasibility of using dynamic network measures to predict personality traits. Using the electro-encephalography (EEG)/magneto-encephalography (MEG) source connectivity method combined with a sliding window approach, dynamic functional brain networks were reconstructed from two datasets: (1) resting-state EEG data acquired from 56 subjects; (2) resting-state MEG data provided from the Human Connectome Project. Then, several dynamic functional connectivity metrics were evaluated. Similar observations were obtained by the two modalities (EEG and MEG) according to the neuroticism, which showed a negative correlation with the dynamic variability of resting-state brain networks. In particular, a significant relationship between this personality trait and the dynamic variability of the temporal lobe regions was observed. Results also revealed that extraversion and openness are positively correlated with the dynamics of the brain networks. These findings highlight the importance of tracking the dynamics of functional brain networks to improve our understanding about the neural substrates of personality.

Design and Study UAV Data Link Terminal with One Station Controls Several Vehicles Dynamic Networking

Considering that there are UAVdynamic networking and collaborative communication requirements under complex mission planning conditions, this paper designs a UAV data link communication terminal with One Station Controls Several Vehicles dynamic networking. Firstly, this paper analyzes the structure of One Station Controls Several Vehicles dynamic networking and cooperative communication system in UAV data link, and combines the characteristics of dynamic networking and task cooperative communication to design a One Station Controls Several Vehicles dynamic networking communication protocol stack and design the structure and function of the man-machine data link, the terminal device hardware is realized by the FPGA chip. This paper focuses on digital zero-IF signal processing unit design and hardware implementation process. Finally, combined with the terminal to build an indoor test environment, this paper tests the network function and performance. The test results prove that the UAV data link terminal in One Station Controls Several Vehicles dynamic networking is effective, and it is practical.

Dynamic Polymer Network System Mediated by Radically Exchangeable Covalent Bond and Carbolong Complex.

It is appealing to develop dynamic polymer systems with multifunctionl properties. Herein, we report a polyurethane elastomer with a dynamic covalent polymer network containing a radically exchangeable 2-arylindane-l,3-dione dimer as thermally sensitive and reversible cross-links. In addition, the carbolong complex, an excellent photothermal agent, is incorporated into the dynamic network backbone. With the irradiation of NIR light, the carbolong complex rapidly generates thermal energy, which subsequently triggers the cleavage of the dynamic covalent bond to generate radicals and activate the polyurethane network. In proof-of-concept experiments, we demonstrate that the utility of a combination of radically exchangeable covalent bond and carbolong moiety brings multiple functional characteristics to the polymer network with a capability of spatiotemporal control, including thermochromism, photochromism, rewritability, malleability, and self-healing. This study holds potentials for exploring more tunable dynamics and improved material properties.

Impulsive and pinning control synchronization of Markovian jumping complex dynamical networks with hybrid coupling and additive interval time-varying delays

This study examines the problem of impulsive and pinning control synchronization of Markovian jumping master-slave complex dynamical networks with hybrid coupling and additive interval time-varying delays. The linear couplings include both the discrete time-varying delay and the distributed time-varying delays. Two kinds of control schemes are utilized to synchronize the considered dynamical network system. Impulsive and pinning control strategies are designed to synchronize the master-slave complex networks. By applying Lyapunov stability theory, Jensen’s inequality, Schur complement and linear matrix inequality technique, some new delay-dependent conditions are derived to guarantee the asymptotic stability of this system. We provided numerical examples to illustrate the feasibility and effectiveness of the results obtained.

Quiver Representations and Dimension Reduction in Dynamical Systems

Dynamical systems often admit geometric properties that must be taken into account when studying their behavior. We show that many such properties can be encoded by means of quiver representations. These properties include classical symmetry, hidden symmetry, and feedforward structure, as well as subnetwork and quotient relations in network dynamical systems. A quiver equivariant dynamical system consists of a collection of dynamical systems with maps between them that send solutions to solutions. We prove that such quiver structures are preserved under Lyapunov--Schmidt reduction, center manifold reduction, and normal form reduction.

Disconnection-aware Attack Detection in Networked Control Systems

This study deals with security issues in dynamical networked control systems. The goal is to establish a unified framework of the attack detection stage, which includes the four processes of monitoring the system state, making a decision based on the monitored signal, disconnecting the corrupted subsystem, and operating the remaining system during restoration. This paper, in particular, considers a disconnection-aware attack detector design problem. Traditionally, observer-based attack detectors are designed based on the system model with a fixed network topology and cannot cope with a change of the topology caused by disconnection. The disconnection-aware design problem is mathematically formulated and a solution is proposed in this paper. A numerical example demonstrates the effectiveness of the proposed detector through an inverter-based voltage control system in a benchmark model.

Design of Controller and Observer for Dynamical Network Systems Based on Weighted Degrees

In this paper, stability conditions based on graph theory for dynamical network systems are shown. Although many frameworks based on graph theory for analysis of dynamical systems have been proposed, there is no stability condition that can be utilized to design of controllers and observers for linear dynamical systems. In this work, to show the stability condition based on graph theory for control and estimation, the dynamical system is represented by a directed graph with weights. The proposed stability conditions are obtained as the inequality of the weighted degrees defined in this paper. As applications, equilibrium point analysis of Lotka-Volterra system and design of pinning controllers and observers for consensus systems are proposed.

Controllability maximization of large-scale systems using projected gradient method

In this work, we formulate two controllability maximization problems for large-scale networked dynamical systems such as brain networks: The first problem is a sparsity constraint optimization problem with a box constraint. The second problem is a modified problem of the first problem, in which the state transition matrix is Metzler. In other words, the second problem is a realization problem for a positive system. We develop a projected gradient method for solving the problems, and prove global convergence to a stationary point with locally linear convergence rate. The projections onto the constraints of the first and second problems are given explicitly. Numerical experiments using the proposed method provide non-trivial results. In particular, the controllability characteristic is observed to change with increase in the parameter specifying sparsity, and the change rate appears to be dependent on the network structure.

Characterizing Network Controllability and Observability for Abstractions and Realizations of Dynamic Networks

One method for managing the complexity of a dynamic network is to abstract some of this complexity away by using a simpler, yet behaviorally equivalent, mathematical model. A theory for such abstractions is currently under development (cf. Kivits and Van den Hof (2018) as well as Woodbury and Warnick (2019)). While recent work has considered concepts of controllability and observability for networked dynamic systems (cf. Xiang et al. (2019) and Liu and Barabási (2016)), this paper analyzes these concepts for abstractions of dynamic networks. In particular, we present the notion of a complete abstraction and an extraneous realization of a dynamic network and show that these concepts characterize the controllability and observability properties of a class of abstractions of dynamic networks.

Formulation of Pruning Maps with Rhythmic Neural Firing

Rhythmic neural firing is thought to underlie the operation of neural function. This triggers the construction of dynamical network models to investigate how the rhythms interact with each other. Recently, an approach concerning neural path pruning has been proposed in a dynamical network system, in which critical neuronal connections are identified and adjusted according to the pruning maps, enabling neurons to produce rhythmic, oscillatory activity in simulation. Here, we construct a sort of homomorphic functions based on different rhythms of neural firing in network dynamics. Armed with the homomorphic functions, the pruning maps can be simply expressed in terms of interactive rhythms of neural firing and allow a concrete analysis of coupling operators to control network dynamics. Such formulation of pruning maps is applied to probe the consolidation of rhythmic patterns between layers of neurons in feedforward neural networks.

Sparse DCM for whole-brain effective connectivity from resting-state fMRI data

Contemporary neuroscience has embraced network science and dynamical systems to study the complex and self-organized structure of the human brain. Despite the developments in non-invasive neuroimaging techniques, a full understanding of the directed interactions in whole brain networks, referred to as effective connectivity, as well as their role in the emergent brain dynamics is still lacking. The main reason is that estimating brain connectivity requires solving a formidable large-scale inverse problem from indirect and noisy measurements. Building on the dynamic causal modelling framework, the present study offers a novel method for estimating whole-brain effective connectivity from resting-state functional magnetic resonance data. To this purpose sparse estimation methods are adapted to infer the parameters of our novel model, which is based on a linearized, region-specific haemodynamic response function. The resulting algorithm, referred to as sparse DCM, is shown to compare favorably with state-of-the art methods when tested on both synthetic and real data. We also provide a graph-theoretical analysis on the whole-brain effective connectivity estimated using data from a cohort of healthy individuals, which reveals properties such as asymmetry in the connectivity structure as well as the different roles of brain areas in favoring segregation or integration.

Cluster synchronization for a class of complex dynamical network system with randomly occurring coupling delays via an improved event-triggered pinning control approach

This paper discusses the cluster synchronization problem for a class of complex dynamical networks with coupling time delays. Under the randomly occurring coupling time delays condition, a novel complex network model is established to express the dynamical behavior of the nodes more precisely. An improved event-triggered mechanism is proposed for two purpose containing the reduction of network burden and improvement of cluster synchronization efficiency. The pinning control strategy is adopted for cluster synchronization via controlling a small fraction of the network nodes. By employing Lyapunov–Krasovskii functional method, a stability criterion is obtained to ensure the achievement of cluster synchronization and a event-triggered pinning controller is constructed. Finally, a simulation example is expressed to verify the effectiveness of our main results.