Conditions For Networks Research Articles

A New Stability Condition for Uncertain Fuzzy Hopfield Neural Networks with Time-varying Delays

In this paper, the global asymptotic stability of uncertain fuzzy Hopfield neural networks(UFHNNs) with time-varying delays is investigated. Firstly, a new fuzzy Lyapunov function comprising a special line-integral function of fuzzy vector is proposed. Then by using the Wirtinger-based integral inequality to determine the upper bound of the derivative term of the Lyapunov function more accurately, a new stability criterion with less conservatism is derived in the form of linear matrix inequality(LMI). At last, an examples is given to show the effectiveness and superiority of our result.

Nonblocking Multicast Networks for Transporting Stream Media

Leaf-spine architecture has been widely adopted as a scalable multistage network. However, for media transport purposes, nonblocking conditions for any combination of multicasts should be taken into account. In this paper, a new approach for building three-stage Clos networks with nonblocking multicast capability is proposed. First, a wide-sense nonblocking (WSNB) condition and a rearrangeable nonblocking (RNB) condition for nonblocking multicast networks are presented. The proposed conditions focus on the distribution of inputs at the middle stage rather than the distribution at the output stage. Second, the proposed conditions are evaluated by mapping to leaf-spine networks with commodity building block switches. The network size is evaluated by calculating the sum of the required building block switches. In the best case of the evaluation results, up to 50% of the switches can be reduced compared with the best-known WSNB condition, and the proposed WSNB networks show good coverage in relatively small but practical network sizes. The proposed RNB networks always show better results than the known RNB multicast conditions.

A unifying approach to nonblocking Clos-like networks with k multiplexing levels

Many multiplexing technologies have been proposed to meet the need for high network capacity. One can foresee that transmission systems with many multiplexing levels will be used in telecommunication networks in the future, and the need for switching connections to pass through multiplexed fiber links will rise accordingly. One Clos-like network with k multiplexing levels was proposed in an earlier work, and the work proved only the strictly nonblocking (SNB) conditions. In this paper, we propose a unifying method to prove not only the SNB condition, but also rearrangeable, repackable and wide-sense nonblocking conditions for the Clos-like network with k multiplexing levels. Note that the proposed new proof for the SNB condition is more compact than that given in the earlier work.

Resilient consensus with switching networks and heterogeneous agents

The resilient consensus problem is investigated for heterogeneous multi-agent systems composed of first-order and second-order agents over randomly switching topologies. The term resilient points to control protocols considering the presence of attacks by malicious agents in the network. By assuming that the maximum number of malicious agents in the network or the neighborhood is known, a distributed consensus protocol based on the notion of network robustness is proposed. Sufficient conditions for switching communication networks over a bounded interval are derived to guarantee that agents can resiliently reach an agreement. Furthermore, the robustness of a network can be significantly improved without additional links between agents after setting a small subset of agents as trusted agents. Numerical simulations are provided to illustrate the effectiveness of the proposed method.

Collision-Prevention Conditions for Wireless Personal Area Networks

In this Letter, we present a theoretical investigation for collision occurrence between adjacent IEEE 802.15.4 wireless personal area networks (WPANs), thus laying the foundation for collision-prevention approaches. Specifically, we identify and present the necessary and sufficient conditions to prevent collisions. The identified conditions can be used to devise collision-prevention mechanisms and estimate WPANs collision probabilities.

Diffusion-dynamics laws in stochastic reaction networks.

Many biological activities are induced by cellular chemical reactions of diffusing reactants. The dynamics of such systems can be captured by stochastic reaction networks. A recent numerical study has shown that diffusion can significantly enhance the fluctuations in gene regulatory networks. However, the universal relation between diffusion and stochastic system dynamics remains veiled. Within the approximation of reaction-diffusion master equation (RDME), we find general relation that the steady-state distribution in complex balanced networks is diffusion-independent. Here, complex balance is the nonequilibrium generalization of detailed balance. We also find that for a diffusion-included network with a Poisson-like steady-state distribution, the diffusion can be ignored at steady state. We then derive a necessary and sufficient condition for networks holding such steady-state distributions. Moreover, we show that for linear reaction networks the RDME reduces to the chemical master equation, which implies that the stochastic dynamics of networks is unaffected by diffusion at any arbitrary time. Our findings shed light on the fundamental question of when diffusion can be neglected, or (if nonnegligible) its effects on the stochastic dynamics of the reaction network.

Networks with diagonal controllability Gramian: Analysis, graphical conditions, and design algorithms

This paper aims to establish explicit relationships between the controllability degree of a network, that is, the control energy required to move the network between different states, and its graphical structure and edge weights. As it is extremely challenging to accomplish this task for general networks, we focus on the case where the network controllability Gramian is a diagonal matrix. The main technical contributions of the paper are (i) to derive necessary and sufficient graphical conditions for networks to feature a diagonal controllability Gramian, and (ii) to propose a constructive algorithm to design network topologies and weights so as to generate stable and controllable networks with pre-specified diagonal Gramians. The proposed network design algorithm allows for individual assignment of how each node responds to external stimuli, so as to selectively enforce robustness to external disturbances. While relying on the simplifying assumption of a diagonal controllability Gramian, our analysis reveals novel and counterintuitive controllability properties of complex networks. For instance, we identify a class of continuous-time networks where the control energy is independent of their cardinality and number of control nodes (thus disproving existing results based on numerical controllability studies), discuss their stability margin, and show that the energy required to control a node can be made independent of its graphical distance from the control nodes. These results complement and formally support, or challenge, a series of conjectures based on numerical studies in the field of complex networks.

Stable Allocations with Network-Based Comparisons

Economic agents often care about their relative well-being: they compare themselves with their neighbors in a social network. In this case, what net- work structures permit stable allocations? We construct a model in which an agent’s utility depends on the ranking of their allocation among those of their network neighbors. An allocation is α-stable if it is not revoked under α-majority voting. We find a sufficient and necessary condition for a network to permit any α-stable allocation: the network has an independent set whose size is at least 1−α of the population size. We provide several comparative statics results for Erdos–Renyi random networks: as networks become more connected, more populated, or more homophilous, they are less permissive; i.e., they permit stable allocations for a smaller set of α. We generalize this model to allow for arbitrary sets of blocking coalitions and provide a sufficient and necessary condition for permissive networks in this case. We also show that our characterization of permissive networks are robust to several variations of the preferences. Other extensions of the model concern directed networks and comparisons made to non-neighbors.

Synchronisation analysis for stochastic T–S fuzzy complex networks with coupling delay

ABSTRACTIn this paper, we investigated synchronisation problem for stochastic Takagi–Sugeno (T-S) fuzzy complex networks model with discrete and distributed time delays. By constructing a new Lyapunov functional and employing Kronecker product, we developed delay-dependent synchronisation criterions. By applying stochastic analysis techniques, we derive starting conditions for synchronisation complex networks of the addressed with mixed time-varying delays and stochastic disturbances are achieved. A numerical examples are provided to demonstrate the effectiveness and usefulness of the proposed results.

Passivity Analysis and Pinning Control of Multi-Weighted Complex Dynamical Networks

A multi-weighted network model with different dimensions of output and input vectors is studied in this paper. First, we analyze the passivity of the proposed network model by employing some inequality techniques and Lyapunov functional method, and give a synchronization condition for output-strictly passive complex dynamical network with multi-weights (CDNMWs). Furthermore, by using pinning adaptive strategies to control a small portion of nodes or edges, some sufficient conditions for ensuring passivity of CD-NMWs are presented. In addition, when CDNMWs under the designed pinning adaptive control strategies are output-strictly passive, two synchronization criteria are also established. Finally, two examples are given to show the validity of the obtained results.

Consensus and Eigenvalue Estimation in Dynamic Consensus Networks with Strictly Positive Real Systems

The use of consensus networks in networking has received great attention due to its wide array of applications in fields such as robotics, transportation, sensor networking, communication networking, biology, and physics. The focus of this paper is to study a generalization of consensus problems whereby the weights of network edges are no longer static gains, but instead are dynamic systems, leading to the notion of dynamic consensus networks. Specifically, we consider networks whose nodes are transfer functions (typically integrators) and whose edges are strictly positive real transfer functions representing dynamical systems that couple the nodes. We transform each concept of static graph theory into dynamic terms, out of which a generalized dynamic graph theory naturally emerges. We present a framework for dynamic graphs and dynamic consensus networks. This framework introduces the idea of dynamic degree, adjacency, incident, and Laplacian matrices in a way that naturally extends these concepts from the static case. We show that strictly positive realness of the edges is a sufficient condition for dynamic networks to be stable (i.e., to reach consensus). To study the spectral properties of dynamic networks, we introduce the Dynamic Grounded Laplacian matrix, which is used to estimate lower and upper bounds for the real parts of the smallest and largest non-zero eigenvalues of the dynamic Laplacian matrix. These bounds can be used to obtain stability conditions using the Nyquist graphical stability test for undirected dynamic networks controlled using distributed controllers. Numerical simulations are provided to verify the effectiveness of the results.

Persistence In Chemical Reaction Networks With Arbitrary Time Delays

We give a sufficient condition for a chemical reaction network with time delays to be persistent, that is, any positive solution to the delay differential equation describing the time evolution of ...

Correction to: Virus propagation: threshold conditions for multiple profile networks

In the original publication, part figures were incorrectly positioned in Figure 2. The correct figure is given below.

Global Asymptotic Stability and Stabilization of Long Short-Term Memory Neural Networks with Constant Weights and Biases

In this paper, a global asymptotic stability condition for Long Short-Term Memory neural networks is presented. Since this condition is formulated in terms of the networks’ weight matrices and biases that are essentially control variables, the same condition can be viewed as a way to globally asymptotically stabilize these networks. The condition and how to compute numerical values for the weight matrices and biases are illustrated by a number of numerical examples.

Parallel routing in regular networks with faults

With the continuous increasing the scale of networks, routing in networks with faulty processors has become inevitable. Motivated by parallel routing in networks with faults, we investigate the fault-tolerant maximally local connectivity of regular networks. A network G is f-fault-tolerant maximally local-connected if each pair of nodes x and y of G−F are connected by min{dG−F(x),dG−F(y)} parallel (node-disjoint) paths for any node subset F of G with |F|≤f, where dG−F(x) and dG−F(y) are the degrees of x and y in G−F, respectively. In this paper, we give a sufficient condition for regular networks to be f-fault-tolerant maximally local-connected. Furthermore, we apply this result on some well-known networks. In addition, several known results about other interconnection networks are straight consequence of our result.

Output synchronization and [formula omitted] output synchronization of complex dynamical networks with multiple derivative couplings

Two types of network models with multiple derivative couplings are investigated in this paper. On one hand, by using matrix theory, Lyapunov functional method and some inequality techniques, several output synchronization conditions for complex dynamical networks with multiple derivative couplings (CDNMDC) are given. Moreover, a adaptive controller is also designed for ensuring the output synchronization of CDNMDC. In addition, we study the H∞ output synchronization of these network models, and some sufficient conditions for guaranteeing H∞ output synchronization of the network models are obtained by employing adaptive control strategy. Eventually, two examples are presented to demonstrate the effectiveness of the derived results.

New stability and stabilization conditions for stochastic neural networks of neutral type with Markovian jumping parameters

This paper discusses the stabilization criteria for stochastic neural networks of neutral type with both Markovian jump parameters. First, delay-dependent conditions to guarantee the globally exponential stability in mean square and almost surely exponential stability of such systems are obtained by combining an appropriate constructed Lyapunov–Krasovskii functional with the semi-martingale convergence theorem. These conditions are in terms of the linear matrix inequalities (LMIs), which can be some less conservative than some existing results. Second, based on the obtained stability conditions, the state feedback controller is designed. Finally, four numerical examples are provided to illustrate the effectiveness and significant improvement of the proposed method.

Passivity and synchronisation of complex dynamical networks with multiple derivative couplings

Two network models with multiple derivative couplings and different dimensions of output and input vectors are investigated in this paper. The problem of passivity for the proposed network models is analysed by utilising some inequality techniques and Lyapunov functional method, and several synchronisation conditions for complex dynamical networks with multiple derivative couplings (CDNMDC) are given. Moreover, by employing adaptive state feedback control strategy, some sufficient conditions for guaranteeing passivity and synchronisation of CDNMDC are obtained. In the end, we give two examples to verify the effectiveness of the results.

Virus propagation: threshold conditions for multiple profile networks

Imagine that we have a highly competing virus that is spreading over a (e.g., social) network where users have different sensitivity/interest against it. A virus may be anything that has a “spreading” behavior such as a rumor, a social media trend or even an infectious disease. Is it possible to predict the outcome in such a viral phenomenon and compute the number of users that will eventually get infected? We answer this question by providing qualitative and quantitative thresholds that describe the behavior of the virus in a given network. Our main contribution is that for the first time, the case of a heterogeneous (with respect to the nodes) network is analytically tackled. We model the different sensitivity to the virus by dividing the nodes of the network into different groups. Each group has a particular profile describing its behavior toward the virus. Conditions are provided based on certain network characteristics that govern the extent of the infection. These conditions are experimentally verified by extensive experiments.

A Theory of Solvability for Lossless Power Flow Equations—Part II: Conditions for Radial Networks

This two-part paper details a theory of solvability for the power flow equations in lossless power networks. In Part I, we derived a new formulation of the lossless power flow equations, which we term the fixed-point power flow. The model is parameterized by several graph-theoretic matrices -- the power network stiffness matrices -- which quantify the internal coupling strength of the network. In Part II, we leverage the fixed-point power flow to study power flow solvability. For radial networks, we derive parametric conditions which guarantee the existence and uniqueness of a high-voltage power flow solution, and construct examples for which the conditions are also necessary. Our conditions (i) imply convergence of the fixed-point power flow iteration, (ii) unify and extend recent results on solvability of decoupled power flow, (iii) directly generalize the textbook two-bus system results, and (iv) provide new insights into how the structure and parameters of the grid influence power flow solvability.