Networks Of Dynamical Systems Research Articles

Reaching Non-Negative Edge Consensus of Networked Dynamical Systems.

In this paper, the problem of non-negative edge consensus of undirected networked linear time-invariant systems is addressed by associating each edge of the network with a state variable, for which a distributed algorithm is constructed. Sufficient conditions referring only to the number of edges are derived for non-negative edge consensus of the networked systems. Subsequently, the linear programming method and a low-gain feedback technique are introduced to simplify the design of the feedback gain matrix for achieving the non-negative edge consensus. It is found that the low-gain feedback technique has a good effect on the non-negative edge consensus of the networked systems subject to input saturation. Numerical simulations are presented to verify the effectiveness of the theoretical results.

A performance evaluation of routing protocols for vehicular ad hoc networks with swarm intelligence

Swarm intelligence work on artificial intelligence which is defined as collective behavior of self organized but centralized system. Movie effect, swarm robotics and network routing are applications of swarm intelligence. Vehicular ad-hoc network (VANET) is also self controlled, high dynamic network system. Road safety and traffic management are the main applications of VANETs. If we integrate swarm intelligence with VANETs, it will show outstanding results in terms of latency, throughput, data delivery cost and ratio. There are some issues in VANETs like data aging, heavy cost and message prioritization which can be solved with the help of swarm intelligence. In this paper, we will come across some good results in VANET when we apply some algorithm of swarm intelligence. There are some algorithms of swarm intelligence that can be applied in VANETs like artificial bee colony and AntNet. Swarm intelligence can be implemented in multicasting and data center routing. Moreover, we will also analysis AODV, DSR routing protocol with the smarm intelligence routing protocol in the network.

Event-Triggered Sliding-Mode Control for Multi-Area Power Systems

This paper solves the load frequency control problem and proposes a new event-triggered sliding-mode control (SMC) algorithm in multi-area interconnected power systems. First, we consider a three-area interconnected power system, and construct its corresponding mathematical model. The prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> , or energy-to-energy, performance is utilized to test the effectiveness of the corresponding disturbance attenuation. Then, an appropriate discrete-time integral switching surface is designed for each subsystem, and the discontinuous controller is designed to guarantee the resulting subsystem asymptotically stable and robust. Using time-delay system analysis technique, the event-triggered scheme, sliding mode dynamics, and the network-induced delays are converted into a network dynamic system with time-varying delays. Thus, corresponding sufficient conditions are derived and an event-triggered SMC law for reaching motion is designed to ensure the reachability of the sliding mode surface in a finite time. Finally, examples and simulations are provided to illustrate the feasibility and the effectiveness of the developed event-triggered SMC scheme.

Controllability Analysis for a Networked Dynamic System With Autonomous Subsystems

This technical note investigates the controllability of networked dynamic systems of which some subsystems are not directly affected by external inputs (i.e., autonomous). The topology can be arbitrary, and every subsystem can have different dynamics and even different number of states, inputs and outputs. We show that to guarantee the controllability of the whole system, every subsystem should be controllable when isolated. We establish some necessary and sufficient conditions for the system to be controllable. These conditions essentially depend on the parameters of every subsystem separately or the strongly connected autonomous subsystems, which reduce significantly computation complexity for large-scale networked systems. We reveal that heterogenous networked systems under some assumptions can be separated into several independent subnetworks, such that the controllability of the whole system is equal to the controllability of each subnetwork. Based on these conditions, criteria that can be easily verified are given for the controllability of networked systems with some special topologies.

Fault Tolerant Algorithms for Multiple Infrastructure Provider Cooperation in Network Virtualization Environment Based on Auctioning

The multiple infrastructure provider network virtualization system is a self-governing system that independently figures out the appropriate number of infrastructure providers and selects the most suitable infrastructure providers in the group to map the virtual network request. This work applies a fault tolerant market-based strategy for efficient working of a network virtualization environment by cooperation of multiple infrastructure providers while dealing with restricted or absolute failures of infrastructure providers during embedding in an unknown, random and dynamic virtual network system. The approach uses auctioning mechanism to decide on the infrastructure provider to serve the virtual network requests, sent by the service providers. A request can be mapped either by a single infrastructure provider or cooperatively by multiple infrastructure providers, depending on the requirements of the service provider’s request and the network resources available with the infrastructure provider. The infrastructure provider that matches best the demands of the service provider is chosen by the system. The feasibility of the proposed methodology is tested by implementing the approach on a group of multiple infrastructure providers that participate in the auctioning mechanism to serve multiple service providers’ virtual network requests.

Multiple-node basin stability in complex dynamical networks.

Dynamical entities interacting with each other on complex networks often exhibit multistability. The stability of a desired steady regime (e.g., a synchronized state) to large perturbations is critical in the operation of many real-world networked dynamical systems such as ecosystems, power grids, the human brain, etc. This necessitates the development of appropriate quantifiers of stability of multiple stable states of such systems. Motivated by the concept of basin stability (BS) [P. J. Menck et al., Nat. Phys. 9, 89 (2013)1745-247310.1038/nphys2516], we propose here the general framework of multiple-node basin stability for gauging the global stability and robustness of networked dynamical systems in response to nonlocal perturbations simultaneously affecting multiple nodes of a system. The framework of multiple-node BS provides an estimate of the critical number of nodes that, when simultaneously perturbed, significantly reduce the capacity of the system to return to the desired stable state. Further, this methodology can be applied to estimate the minimum number of nodes of the network to be controlled or safeguarded from external perturbations to ensure proper operation of the system. Multiple-node BS can also be utilized for probing the influence of spatially localized perturbations or targeted attacks to specific parts of a network. We demonstrate the potential of multiple-node BS in assessing the stability of the synchronized state in a deterministic scale-free network of Rössler oscillators and a conceptual model of the power grid of the United Kingdom with second-order Kuramoto-type nodal dynamics.

Controllability of networked higher-dimensional systems with one-dimensional communication.

In this paper, the state controllability of networked higher-dimensional linear time-invariant dynamical systems is considered, where communications are performed through one-dimensional connections. The influences on the controllability of such a networked system are investigated, which come from a combination of network topology, node-system dynamics, external control inputs and inner interactions. Particularly, necessary and sufficient conditions are presented for the controllability of the network with a general topology, as well as for some special settings such as cycles and chains, which show that the observability of the node system is necessary in general and the controllability of the node system is necessary for chains but not necessary for cycles. Moreover, two examples are constructed to illustrate that uncontrollable node systems can be assembled to a controllable networked system, while controllable node systems may lead to uncontrollable systems even for the cycle topology.This article is part of the themed issue 'Horizons of cybernetical physics'.

Nonnegative Edge Quasi-Consensus of Networked Dynamical Systems

Differing from the existing literature on node consensus, this brief studies consensus taking place on the edges of networked dynamical systems. A distributed edge quasi-consensus protocol is developed to lead the states of all edges to converge into a bounded region. For a connected network with nonnegative initial edge states, it is proved that the edge quasi-consensus can be reached while the states of all edges can be kept nonnegative. Moreover, the nonnegative edge quasi-consensus of networked systems with edge state constraints or input saturation is analyzed, respectively. Numerical simulations are provided to verify the effectiveness of the protocols.

Game-Theoretic Multi-Agent Control and Network Cost Allocation Under Communication Constraints

Multi-agent networked linear dynamic systems have attracted the attention of researchers in power systems, intelligent transportation, and industrial automation. The agents might cooperatively optimize a global performance objective, resulting in social optimization, or try to satisfy their own selfish objectives using a noncooperative differential game. However, in these solutions, large volumes of data must be sent from system states to possibly distant control inputs, thus resulting in high cost of the underlying communication network. To enable economically viable communication, a game-theoretic framework is proposed under the communication cost , or sparsity , constraint, given by the number of communicating state/control input pairs. As this constraint tightens, the system transitions from dense to sparse communication, providing the tradeoff between dynamic system performance and information exchange. Moreover, using the proposed sparsity-constrained distributed social optimization and noncooperative game algorithms, we develop a method to allocate the costs of the communication infrastructure fairly and according to the agents’ diverse needs for feedback and cooperation. Numerical results illustrate utilization of the proposed algorithms to enable and ensure economic fairness of wide-area control among power companies.

Mean-Square Consensus Seeking over Multi-Interconnection Dynamical Networks with Markovian Switching Topologies

This paper considers the mean-square consensus problem for a nonlinear complex dynamical network system with Markovian switching topologies, topology uncertainties and time-varying delays. For the system, each node is a Lure system whose nonlinearity satisfies a sector condition, and more than one interconnections are considered in view of the fact that the subsystems of networks may be multiple interconnected. By using the linear matrix inequality method and the partial stability theory, sufficient conditions of the exponentially mean-square consensus are obtained for the nonlinear complex dynamical network Lure system in the Markovian switching topologies. Moreover, a novel static output controller has been designed to make the system achieve exponentially mean-square consensus successfully. Finally, a numerical example is presented to illustrate the efficiency and applicability of the proposed methods.

Spectral Modes of Network Dynamics Reveal Increased Informational Complexity Near Criticality

What does the informational complexity of dynamical networked systems tell us about intrinsic mechanisms and functions of these complex systems? Recent complexity measures such as integrated information have sought to operationalize this problem taking a whole-versus-parts perspective, wherein one explicitly computes the amount of information generated by a network as a whole over and above that generated by the sum of its parts during state transitions. While several numerical schemes for estimating network integrated information exist, it is instructive to pursue an analytic approach that computes integrated information as a function of network weights. Our formulation of integrated information uses a Kullback-Leibler divergence between the multi-variate distribution on the set of network states versus the corresponding factorized distribution over its parts. Implementing stochastic Gaussian dynamics, we perform computations for several prototypical network topologies. Our findings show increased informational complexity near criticality, which remains consistent across network topologies. Spectral decomposition of the system’s dynamics reveals how informational complexity is governed by eigenmodes of both, the network’s covariance and adjacency matrices. We find that as the dynamics of the system approach criticality, high integrated information is exclusively driven by the eigenmode corresponding to the leading eigenvalue of the covariance matrix, while sub-leading modes get suppressed. The implication of this result is that it might be favorable for complex dynamical networked systems such as the human brain or communication systems to operate near criticality so that efficient information integration might be achieved.

核心边缘网络结构对银行系统稳定性影响研究

银行间网络结构对银行系统的稳定性具有重要的影响，但目前的研究大多以随机网络结构来研究银行系统的稳定性，但是很多实证研究发现核心边缘网络是银行拆借市场的一种重要网络特征，因此本文构建核心边缘网络拓扑模型，然后建立动态演化的银行网络系统模型，从而研究核心边缘网络结构对银行系统稳定性的影响。结果表明：在边缘银行受到存款冲击的情形下，对比随机的网络结构，核心边缘的网络结构会使银行系统更稳定。在核心银行受到存款冲击的情形下，只有当连接度小并且核心银行总数少时，随机网络更稳定；当连接度小且核心银行总数大，或当连接度大时，核心边缘网络更稳定。 The network topology structure of the interbank network has an important effect on the stability of bank system; most of the current researches study the effect of the random network on the stability of bank system. However many empirical investigations find that the core-periphery (CP) is an important network characteristic of the interbank market, therefore, the present paper constructs the CP network structure of the interbank market, and then constructs a dynamical evolutional bank network system model, furthermore studies the effect of CP network structure on the stability of the bank system. The research results show that when the periphery banks suffer from the deposits shocks, the CP network is more stable than the random network. However, when the core banks face the deposits shocks, there are three cases according to the connectivity of the banking system. In the case of the lower connectivity and small number of core banks, then the random network is more stable; in the case of the lower connectivity and big number of core banks, or in the case of the bigger connectivity, the CP network is more stable.

Inferring connectivity in networked dynamical systems: Challenges using Granger causality.

Determining the interactions and causal relationships between nodes in an unknown networked dynamical system from measurement data alone is a challenging, contemporary task across the physical, biological, and engineering sciences. Statistical methods, such as the increasingly popular Granger causality, are being broadly applied for data-driven discovery of connectivity in fields from economics to neuroscience. A common version of the algorithm is called pairwise-conditional Granger causality, which we systematically test on data generated from a nonlinear model with known causal network structure. Specifically, we simulate networked systems of Kuramoto oscillators and use the Multivariate Granger Causality Toolbox to discover the underlying coupling structure of the system. We compare the inferred results to the original connectivity for a wide range of parameters such as initial conditions, connection strengths, community structures, and natural frequencies. Our results show a significant systematic disparity between the original and inferred network, unless the true structure is extremely sparse or dense. Specifically, the inferred networks have significant discrepancies in the number of edges and the eigenvalues of the connectivity matrix, demonstrating that they typically generate dynamics which are inconsistent with the ground truth. We provide a detailed account of the dynamics for the Erdős-Rényi network model due to its importance in random graph theory and network science. We conclude that Granger causal methods for inferring network structure are highly suspect and should always be checked against a ground truth model. The results also advocate the need to perform such comparisons with any network inference method since the inferred connectivity results appear to have very little to do with the ground truth system.

An artificial immune-memory model based on idiotypic immune networks: Perspectives on antibody dynamics

Immune memories of antigens are formed as limit behavior of antibody dynamics, which is a simplified model of cyclic idiotypic immune networks. Rapid responses of immune systems to secondary antigens are due to the memory recalls of the stored antigenic attributes. The immune-memory mechanism is studied by combining network structure and dynamical systems. Moreover, associative memory can be explored by network dynamics of a cross-correlation matrix determined by an antibody chain. Analysis of cross-reactive immune responses can be accomplished by introducing the overlapping difference function ρ of network dynamics. Classification of four types of memory recalls was performed here. It explains the phenomena of associative memory and provides methods for control of vaccinations via tuning of suitable parameters. Other issues with immune memory and cyclic idiotypic immune networks are also discussed.

Bounded invariant verification for time-delayed nonlinear networked dynamical systems

We present a technique for bounded invariant verification of nonlinear networked dynamical systems with delayed interconnections. The underlying problem in precise bounded-time verification lies with computing bounds on the sensitivity of trajectories (or solutions) to changes in initial states and inputs of the system. For large networks, computing this sensitivity with precision guarantees is challenging. We introduce the notion of input-to-state (IS) discrepancy of each module or subsystem in a larger nonlinear networked dynamical system. The IS discrepancy bounds the distance between two solutions or trajectories of a module in terms of their initial states and their inputs. Given the IS discrepancy functions of the modules, we show that it is possible to effectively construct a reduced (low dimensional) time-delayed dynamical system, such that the trajectory of this reduced model precisely bounds the distance between the trajectories of the complete network with changed initial states. Using the above results we develop a sound and relatively complete algorithm for bounded invariant verification of networked dynamical systems consisting of nonlinear modules interacting through possibly delayed signals. Finally, we introduce a local version of IS discrepancy and show that it is possible to compute them using only the Lipschitz constant and the Jacobian of the dynamic function of the modules.

Inferring Biological Networks by Sparse Identification of Nonlinear Dynamics

Inferring the structure and dynamics of network models is critical to understanding the functionality and control of complex systems, such as metabolic and regulatory biological networks. The increasing quality and quantity of experimental data enable statistical approaches based on information theory for model selection and goodness-of-fit metrics. We propose an alternative data-driven method to infer networked nonlinear dynamical systems by using sparsity-promoting optimization to select a subset of nonlinear interactions representing dynamics on a network. In contrast to standard model selection methods-based upon information content for a finite number of heuristic models (order 10 or less), our model selection procedure discovers a parsimonious model from a combinatorially large set of models, without an exhaustive search. Our particular innovation is appropriate for many biological networks, where the governing dynamical systems have rational function nonlinearities with cross terms, thus requiring an implicit formulation and the equations to be identified in the null-space of a library of mixed nonlinearities, including the state and derivative terms. This method, implicit-SINDy, succeeds in inferring three canonical biological models: 1) Michaelis-Menten enzyme kinetics; 2) the regulatory network for competence in bacteria; and 3) the metabolic network for yeast glycolysis.

Distributed state observer design for networked dynamic systems

Two linear matrix inequality (LMI)-based sufficient conditions are derived for stability analysis of networked systems with linear time invariant dynamics, which depend only on the parameters of each subsystem and the subsystem connection matrix. Relations among the new sufficient conditions and the previous one are discussed. Then, a distributed state observer is constructed for networked systems. Several LMI-based conditions are further established to design a completely distributed state observer that can be stabilised by a block diagonal gain matrix. Numerical simulations show that these methods are attractive in the analysis and synthesis of large-scale networked systems.

The case for increasing returns (2): the methods of planning horizons

In neoclassical economics, substitution assumptions support equilibrium models in closed systems shunning interdependence. On these grounds an array of frames show outcomes as stable, efficient, unique and determinate. Heterodox economists say equilibrium models sidestep practical knowledge and the rich reality of economic behavior. Rigor or realism, mainstream or radical, ecological, institutional, socio-cultural: economics invites a wide diversity of assumptions, once short-term models of substitution are opened to question. The answers are blurred by applications; there is clarity in a simplicity shielded from mundane detail. This paper addresses the methodological impact of planning horizons, increasing returns and complementarity, and their proper representation in economic constructions. Horizonal economics can be construed as extending orthodox standards into a realm of time, but for its subtler ramifications. Increasing returns make our relations complementary and not substitutional, loosening the tight deductions from mainstream models of choice. The horizonal extension of our received theory of price applies time to cost and demand curves, showing Marshallian scissors (supply and demand) cut outward and downward with expanded horizons. Static conceptions appear in horizonal groups, suggesting complete theories of price should specify agents’ horizons, with no further radical impact: the trouble emerges with increasing returns and complementarity. Horizons stem from unbounded causality; if all we do ripples outward forever in nature and society, the relevant field of inquiry for economics is interdependent: this is the case for bounded rationality as an analytical limit to economic conceptions. In turn, interdependence suggests a use of network constructs to frame complex systemic cascades, and networks open a door to complementarity and increasing returns in transport and information exchange. The gaping maw of increasing returns and complementarity opens, swallowing down neat traditions such as stability, equilibrium, marginalism, partial analysis, supply and demand depictions of price, etc. The methodological lesson of this shift to network contexts and dynamic complex systems supersedes some of our favored doctrines and the analyses on which they stand. Without decreasing returns and substitution, neoclassical arguments simply do not work. Heterodox approaches – and their intelligent application – are required in this setting. The paper offers a few guidelines to an unexplored domain of fundamental departures.

Using Network Dynamical Influence to Drive Consensus.

Consensus and decision-making are often analysed in the context of networks, with many studies focusing attention on ranking the nodes of a network depending on their relative importance to information routing. Dynamical influence ranks the nodes with respect to their ability to influence the evolution of the associated network dynamical system. In this study it is shown that dynamical influence not only ranks the nodes, but also provides a naturally optimised distribution of effort to steer a network from one state to another. An example is provided where the “steering” refers to the physical change in velocity of self-propelled agents interacting through a network. Distinct from other works on this subject, this study looks at directed and hence more general graphs. The findings are presented with a theoretical angle, without targeting particular applications or networked systems; however, the framework and results offer parallels with biological flocks and swarms and opportunities for design of technological networks.

Kinds versus continua: a review of psychometric approaches to uncover the structure of psychiatric constructs.

The question of whether psychopathology constructs are discrete kinds or continuous dimensions represents an important issue in clinical psychology and psychiatry. The present paper reviews psychometric modelling approaches that can be used to investigate this question through the application of statistical models. The relation between constructs and indicator variables in models with categorical and continuous latent variables is discussed, as are techniques specifically designed to address the distinction between latent categories as opposed to continua (taxometrics). In addition, we examine latent variable models that allow latent structures to have both continuous and categorical characteristics, such as factor mixture models and grade-of-membership models. Finally, we discuss recent alternative approaches based on network analysis and dynamical systems theory, which entail that the structure of constructs may be continuous for some individuals but categorical for others. Our evaluation of the psychometric literature shows that the kinds-continua distinction is considerably more subtle than is often presupposed in research; in particular, the hypotheses of kinds and continua are not mutually exclusive or exhaustive. We discuss opportunities to go beyond current research on the issue by using dynamical systems models, intra-individual time series and experimental manipulations.