Duplex Networks Research Articles

Finite Time Hybrid Synchronization of Heterogeneous Duplex Complex Networks via Time-varying Intermittent Control

Abstract This paper study the finite time internal synchronization and the external synchronization (hybrid synchronization) for duplex heterogeneous complex networks by time-varying intermittent control. There few study hybrid synchronization of heterogeneous duplex complex networks. Therefore, we research the finite time hybrid synchronization of heterogeneous duplex networks, which employs the time-varying intermittent control to drive the duplex heterogeneous complex networks to achieve hybrid synchronization in finite time. To be specific, the switch frequency of the controllers can be changed with time by devise Lyapunov function and boundary function, the internal synchronization and external synchronization are achieved simultaneously in finite time. Finally, numerical examples are presented to illustrate the validness of theoretical results.

Synchronization in a Memristive Duplex Network: The Impact of Intra-layer and Inter-layer Synaptic Pathways

Synchronization in multiplex networks is crucial for modeling functional connectivity in computational neuroscience. This study analyzes synchronization in a memristive Hindmarsh-Rose duplex network, investigating how synaptic pathways affect synchronization. Initially, electrical, inner-linking, and chemical functions are separately applied to both intra- and inter-layer connections. Then, a more realistic approach combines intra-layer electrical and inner-linking functions with inter-layer chemical synapses. Field coupling is also examined as an inter-layer connection with different intra-layer synapses. Synchronization stability is evaluated using the master stability function and synchronization error. Results show that electrical and inner-linking functions support intra- and inter-layer synchronization as coupling strength increases. However, with chemical synapses, neurons achieve synchronization under limited conditions. Applying chemical synapses to inter-layer connections restricts inter-layer synchronization, although intra-layer synchronization remains observable with electrical or inner-linking functions. Field coupling effectively promotes inter-layer synchronization when paired with intra-layer chemical connections but reduces it with intra-layer electrical or inner-linking functions.

A node-based SIRS epidemic model on two-layer interconnected networks: Dynamical analysis of interplay between layers

From the micro-level perspective of individuals, this paper proposes a node-based SIRS epidemic model on two-layer networks, and investigates the stability of the equilibrium in the model as well as the influence of network structures and infected or recovered rate on disease propagation. By using the stability theory, we give the accurate sufficient condition for the stability as well as the threshold of disease prevalence, showing the threshold of such two-layer network is less than that of isolated single-layer network. Also, an easy-to-use approximate criterion for stability of disease-free equilibrium is provided for the two-layer network with general intra-layer structures when the infected rate across layers is far less than that within layers. Further, extensive numerical simulations on several classical network structure models verify the theoretical results, and show some new interesting results: (1) for the duplex network with equivalent number of connections each layer, the infected rate across layers has more significant effect on epidemic spreading than that within layers; (2) when fixing the whole network edge density, the same number of connections each layer always be the most conductive to propagate of the disease for the duplex network of ER structures, but it is the most/worst conductive to propagate at large/small infected rate for the duplex network of small-world structures.

Synchronization on Directed Delayed Duplex Networks: From the Perspective of Coupled Delays

Synchronization on Directed Delayed Duplex Networks: From the Perspective of Coupled Delays

Practical generalized finite-time synchronization of duplex networks with quantized and delayed couplings via intermittent control

<abstract><p>This paper investigates the practical generalized finite-time synchronization (PGFETS) of duplex networks with quantized and delayed couplings. Given that continuous transmission of signals will increase the load and cost of communication, we introduce quantized couplings in the model. Then, via the theorem of finite-time stability, the PGFETS is proposed based on the fact that PGFETS is much more extensive and practical than classical finite-time synchronization. Some sufficient criteria are formulated to achieve the goal of synchronization by utilizing quantized intermittent control schemes. Lastly, the validity of the theoretical results is illustrated by numerical simulations.</p></abstract>

Q-neighbor Ising model on multiplex networks with partial overlap of nodes.

The q-neighbor Ising model for the opinion formation on multiplex networks with two layers in the form of random graphs (duplex networks), the partial overlap of nodes, and LOCAL&AND spin update rule was investigated by means of the pair approximation and approximate master equationsas well as Monte Carlo simulations. Both analytic and numerical results show that for different fixed sizes of the q-neighborhood and finite mean degrees of nodes within the layers the model exhibits qualitatively similar critical behavior as the analogous model on multiplex networks with layers in the form of complete graphs. However, as the mean degree of nodes is decreased the discontinuous ferromagnetic transition, the tricritical point separating it from the continuous transition, and the possible coexistence of the paramagnetic and ferromagnetic phases at zero temperature occur for smaller relative sizes of the overlap. Predictions of the simple homogeneous pair approximation concerning the critical behavior of the model under study show good qualitative agreement with numerical results; predictions based on the approximate master equationsare usually quantitatively more accurate but yet not exact. Two versions of the heterogeneous pair approximation are also derived for the model under study, which, surprisingly, yield predictions only marginally different or even identical to those of the simple homogeneous pair approximation. In general, predictions of all approximations show better agreement with the results of Monte Carlo simulations in the case of continuous than discontinuous ferromagnetic transition.

Few-shot segmentation with duplex network and attention augmented module.

Establishing the relationship between a limited number of samples and segmented objects in diverse scenarios is the primary challenge in few-shot segmentation. However, many previous works overlooked the crucial support-query set interaction and the deeper information that needs to be explored. This oversight can lead to model failure when confronted with complex scenarios, such as ambiguous boundaries. To solve this problem, a duplex network that utilizes the suppression and focus concept is proposed to effectively suppress the background and focus on the foreground. Our network includes dynamic convolution to enhance the support-query interaction and a prototype match structure to fully extract information from support and query. The proposed model is called dynamic prototype mixture convolutional networks (DPMC). To minimize the impact of redundant information, we have incorporated a hybrid attentional module called double-layer attention augmented convolutional module (DAAConv) into DPMC. This module enables the network to concentrate more on foreground information. Our experiments on PASCAL-5i and COCO-20i datasets suggested that DPMC and DAAConv outperform traditional prototype-based methods by up to 5-8% on average.

A Topological Mechanism of Superdiffusion on Duplex Networks

Superdiffusion is an interesting phenomenon from both theoretical and practical perspectives. We propose a sufficient condition for the occurrence of superdiffusion on duplex networks by applying the generating functionology from combinatorial mathematics. Our result indicates that, with fixed values of intra-layer diffusion constants, superdiffusion emerges from a certain combination of different network topologies, which provides a topological mechanism to regulate the whole diffusion process. On a more general ground, we provide two inter-layer linking strategies to expand the applicability of the above topological mechanism on real-world networks, and construct a class of specific duplex networks on which superdiffusion occurs. We further verify that diffusion with negative inter-layer correlation is faster than those with positive correlation from a typical duplex structure. Given the ubiquity of diffusion in the real world, our results constitute a significant step toward a better understanding of superdiffusion processes on multiplex networks.

A dynamics model of knowledge dissemination in a WeChat Group from perspective of duplex networks

Studying how to promote knowledge dissemination in a WeChat group is of great significance to organizational knowledge management in China. There are two different ways for group members disseminating a certain knowledge: just sharing it in WeChat group (many-to-many dissemination mode), or using @username function to disseminate it (point-to-point dissemination mode). We regard all group members connected by relationships of two different dissemination modes in a WeChat group as duplex networks. We build a susceptible-infected-recovered-immune (sirm) dynamics model of knowledge dissemination in the duplex networks to obtain the basic reproduction number R0 of a certain knowledge transmission. We use the actual data to estimate the parameters of this model, and verify that our model fits well with the actual data. The numerical simulations show that: 1) The total number of times that members communicate a certain knowledge via two modes per unit time should not be excessive, to avoid fatigue to it which resulting low efficiency of dissemination in the WeChat group. 2) If the benefit obtained by group members from learning a certain knowledge is higher than the required variable cost, the kind of knowledge is likely to be spread in the WeChat group. If a certain knowledge becomes obsolete or is updated for some group members, they will not disseminate it even after they have learned it and it may gradually disappear in the WeChat group. 3) When members only use either point-to-point @mention function discussion or many-to-many random communication to transmit a certain knowledge, or there is big difference in the number of times that group members use each of the above two discussion modes per unit time, the efficiency of the knowledge dissemination is reduced in a WeChat group.

Dynamics of corruption on correlated multiplex networks with overlap

To get further insight into the mechanism behind driving the social behaviors for a compartmental flow model of corruption on multiplex networks, we apply the model to the duplex networks, where different flows among three states (Honest, Corrupt, Ostracism) take place separately on a particular layer. In our work, we aim to unravel the impact of edge overlap and interlayer degree correlations on the evolution of corruption by considering different underlying contact networks. To assess the role of the edge overlap (m) on the diffusion of corruption, we produce various values of m by rewiring the edges of one of two synthetic networks. In addition, to explore the significance of interlayer degree correlations, we generate the duplex networks with specific degree correlated patterns giving rise to different values of m. The results show that the influence of the structural properties becomes gradually prominent as the corruption and delation rate decrease. The smaller m produced by rewiring the biased edges makes the extension of the stability region of full honesty state though not clearly noticeable. However, the larger m determined by the degree correlation patterns is prone to the presence of the stability region of the full H state. The findings reveal that edge overlap caused by rewiring links barely has an effect on the evolution regardless of duplex networks being uncorrelated or correlated. Nevertheless, the interlayer correlated coupling plays a major role in the stationary states of the corruption dynamics.

Interlayer antisynchronization in degree-biased duplex networks.

With synchronization being one of nature's most ubiquitous collective behaviors, the field of network synchronization has experienced tremendous growth, leading to significant theoretical developments. However, most previous studies consider uniform connection weights and undirected networks with positive coupling. In the present article, we incorporate the asymmetry in a two-layer multiplex network by assigning the ratio of the adjacent nodes' degrees as the weights to the intralayer edges. Despite the presence of degree-biased weighting mechanism and attractive-repulsive coupling strengths, we are able to find the necessary conditions for intralayer synchronization and interlayer antisynchronization and test whether these two macroscopic states can withstand demultiplexing in a network. During the occurrence of these two states, we analytically calculate the oscillator's amplitude. In addition to deriving the local stability conditions for interlayer antisynchronization via the master stability function approach, we also construct a suitable Lyapunov function to determine a sufficient condition for global stability. We provide numerical evidence to show the necessity of negative interlayer coupling strength for the occurrence of antisynchronization, and such repulsive interlayer coupling coefficients cannot destroy intralayer synchronization.

Fixed-time synchronization of switched duplex networks with stochastic disturbances and limited communication

This paper investigates the issue of fixed-time intralayer synchronization of stochastic switched duplex networks (SSDNs) with limited communication. Firstly, control scheme without sign function is created to explore intralayer synchronization of SSDNs within a fixed time, and the control gains can vary with the error information. By the Lyapunov functional method, some novel synchronization criteria are established. In addition, by means of introducing the channel matrices, this paper considers the limited communication. Moreover, numerical simulation indicates the correctness of our theoretical result. Finally, from the perspective of the application, image encryption is demonstrated to confirm our theoretical implementation.

Superdiffusion induced by complete structure in multiplex networks.

After the groundbreaking work by Gómez et al., the superdiffusion phenomenon on multiplex networks begins to attract researchers' attention. The emergence of superdiffusion means that the time scale of the diffusion process of the multiplex network is shorter than that of each layer. Using the optimization theory, the manuscript studies the greatest impact of one edge on the network diffusion speed. It is proved that by deleting any edge from a given network, the drop of the second smallest eigenvalue of its Laplacian matrix is at most 2. Based on the conclusion, the relation between the complete structure and the superdiffusible network is studied, and, further, some superdiffusion criteria on general duplex networks are proposed. Interestingly, the theoretical results indicate that the emergence of superdiffusion depends on the complete structure rather than the overlap one. Some numerical examples are shown to verify the effectiveness of the theoretical results.

Coding in Diffusion-Based Molecular Nanonetworks: A Comprehensive Survey

Diffusion-based molecular nanonetworks exploit the diffusion of molecules, e.g., in free space or in blood vessels, for the purpose of communication. This article comprehensively surveys coding approaches for communication in diffusion-based molecular nanonetworks. In particular, all three main purposes of coding for communication, namely source coding, channel coding, and network coding, are covered.We organize the survey of the channel coding approaches according to the different channel codes, including linear block codes, convolutional codes, and inter-symbol interference (ISI) mitigation codes. The network coding studies are categorized into duplex network coding, physical-layer network coding, multi-hop nanonetwork coding, performance improvements of network-coded nanosystems, and network coding in mobile nanonetworks. We also present a comprehensive set of future research directions for the still nascent area of coding for diffusion-based molecular nanonetworks; specifically, we outline research imperatives for each of the three main coding purposes, i.e., for source, channel, and network coding, as well as for overarching research goals.

Finite Time Inter-Layer Synchronization of Duplex Networks via Event-Dependent Intermittent Control

This brief is devoted to the finite time inter-layer synchronization of duplex networks by means of intermittent control. Different from most previous works, the intermittent control scheme devised is an event-dependent type, which relaxes the strict constraints of control time. To be specific, the work time of intermittent controller is no longer set in advance, and determined by the relation between the designed Lyapunov function and two preset boundary functions. Based on the proposed intermittent control mechanism, a sufficient condition is given to guarantee the finite time inter-layer synchronization of the duplex networks. Finally, numerical examples are presented to illustrate the validness of theoretical results.

A dynamics model of two kinds of knowledge transmission on duplex networks

First, we consider the complex system composed of two kinds of knowledge transmitted by individuals in an organization as a set of duplex networks, which including two sub-networks, one consisting of individuals disseminating one kind of knowledge through online and offline channels, and the other sub-network consisting of individuals disseminating the other kind of knowledge through the two channels. On this basis, we establish a s1i1r1i1−s2i2r2i2 dynamics model of two kinds of knowledge transmission on duplex networks. Second, we obtain the threshold to distinguish whether one kind of knowledge is continuously spread or not through the two channels in the organization, and verify that our model fits well with the actual data. Finally, we conduct the numerical simulations on the process of two kinds of knowledge transmission through online and offline channels. The simulations indicate that: (1) If one kind of knowledge is transmitted online too many times for individuals in unit time, it will likely lead to the gradual loss of the other kind of knowledge in the organization. Each kind of knowledge should be disseminated online moderately for individuals so that both kinds of knowledge can be continuously spread. (2) The transmission of each kind of knowledge is more efficient in the scale-free (online)–homogeneous (offline) sub-network when there is facilitation between the dissemination of two kinds of knowledge. When there is competition between two kinds of knowledge dissemination in the same group, the time of transmission to stabilize in the scale-free (online)–homogeneous (offline) sub-network is shorter, but the final scale of transmission in the homogeneous (online)–homogeneous (offline) sub-network is larger for each kind of knowledge.

Hyper-diffusion on multiplex networks

Multiplex networks describe systems whose interactions can be of different nature, and are fundamental to understand complexity of networks beyond the framework of simple graphs. Recently it has been pointed out that restricting the attention to pairwise interactions is also a limitation, as the vast majority of complex systems include higher-order interactions that strongly affect their dynamics. Here, we propose hyper-diffusion on multiplex networks, a dynamical process in which diffusion on each single layer is coupled with the diffusion in other layers thanks to the presence of higher-order interactions occurring when there exists link overlap. We show that hyper-diffusion on a duplex network (a multiplex network with two layers) can be described by the hyper-Laplacian in which the strength of four-body interactions among every set of four replica nodes connected in both layers can be tuned by a parameter δ 11 ⩾ 0. The hyper-Laplacian reduces to the standard lower Laplacian, capturing pairwise interactions at the two layers, when δ 11 = 0. By combining tools of spectral graph theory, applied topology and network science we provide a general understanding of hyper-diffusion on duplex networks when δ 11 > 0, including theoretical bounds on the Fiedler and the largest eigenvalue of hyper-Laplacians and the asymptotic expansion of their spectrum for δ 11 ≪ 1 and δ 11 ≫ 1. Although hyper-diffusion on multiplex networks does not imply a direct ‘transfer of mass’ among the layers (i.e. the average state of replica nodes in each layer is a conserved quantity of the dynamics), we find that the dynamics of the two layers is coupled as the relaxation to the steady state becomes synchronous when higher-order interactions are taken into account and the Fiedler eigenvalue of the hyper-Laplacian is not localized in a single layer of the duplex network.

Critical Parameters in Dynamic Network Modeling of Sepsis.

In this work, we propose a dynamical systems perspective on the modeling of sepsis and its organ-damaging consequences. We develop a functional two-layer network model for sepsis based upon the interaction of parenchymal cells and immune cells via cytokines, and the coevolutionary dynamics of parenchymal, immune cells, and cytokines. By means of the simple paradigmatic model of phase oscillators in a two-layer system, we analyze the emergence of organ threatening interactions between the dysregulated immune system and the parenchyma. We demonstrate that the complex cellular cooperation between parenchyma and stroma (immune layer) either in the physiological or in the pathological case can be related to dynamical patterns of the network. In this way we explain sepsis by the dysregulation of the healthy homeostatic state (frequency synchronized) leading to a pathological state (desynchronized or multifrequency cluster) in the parenchyma. We provide insight into the complex stabilizing and destabilizing interplay of parenchyma and stroma by determining critical interaction parameters. The coupled dynamics of parenchymal cells (metabolism) and nonspecific immune cells (response of the innate immune system) is represented by nodes of a duplex layer. Cytokine interaction is modeled by adaptive coupling weights between nodes representing immune cells (with fast adaptation timescale) and parenchymal cells (slow adaptation timescale), and between pairs of parenchymal and immune cells in the duplex network (fixed bidirectional coupling). The proposed model allows for a functional description of organ dysfunction in sepsis and the recurrence risk in a plausible pathophysiological context.

Robust Resource Allocation for Lightweight Secure Transmission in Multicarrier NOMA-Assisted Full Duplex IoT Networks

In this article, with the aim to enhance the secure transmission and improve the utilization of spectrum resources in Internet of Things (IoT), a multicarrier nonorthogonal multiple access (MC-NOMA)-assisted full duplex (FD) network is investigated, in which nonorthogonal multiple access (NOMA) is implemented in both uplink and downlink transmissions. The lightweight and low-power physical layer security (PLS) technology is employed to protect the information from eavesdropping. Taking the imperfect channel state information (CSI) into account, we formulate a problem to optimize the beamforming vector, artificial noise (AN), transmit power, and subcarrier assignment policy aiming to maximize the worst case sum secrecy rate under the Quality of Service (QoS) and power consumption constraints. Since the formulated problem is nonconvex and difficult to be solved, we decompose it into two joint optimization subproblems. The first is resource allocation with given subcarrier assignment, which is solved by using the block coordinate descent (BCD) approach. The second is subcarrier assignment solved by the matching theory. Our simulation shows that the proposed scheme is robust against the CSI imperfectness of the eavesdropping and self-interference channels, while providing significant sum secrecy rate improvement compared with the orthogonal multiple access (OMA), half duplex (HD) systems, and other benchmark schemes.

Network coherence of weighted duplex networks: Exact results

The Laplacian spectra are often used to characterize topological properties and dynamical characteristics of the networks. In this paper, we analytically calculate the network coherence quantified by the Laplacian spectra, which is a measurement of the extent of consensus in the coupled systems with the noise. Due to complex interactions between two coupled networks, we choose three types of weighted duplex networks with an aim of obtaining their exact solutions of the network coherence. Based on the network structures and matrix theories, we provide analytical expressions of the coherence regarding the network size and weights and further study the robustness of the coherence under network parameters. We finally show that smaller network sizes and larger weights will lead to better coherence and the best coherence happens in a duplex network because there are more connections between the layers.