Robustness of multilayer oscillator networks

Analysis of dynamical robustness of multilayer neuronal networks with inter-layer ephaptic coupling at different scales

Robustness of multipartite networks in face of random node failure

Satellite networks have great potential in providing global ubiquitous broadband communication. In this paper, we explore the capacity of both single-layered and two-layered satellite networks. Closed-form approximate expressions of network capacity are derived, which provide insights into the impact of different network parameters, such as number of orbits, number of satellites in each orbit, link bandwidth, existence of the seam, the relative position between the two layers, etc. We investigate the advantages of two-layered structure by comparing the capacity of single-layered and two-layered networks. The results show that the network capacity of two-layered networks is always no less than the total capacity of the two layers. Moreover, we obtain the network parameter condition under which the network capacity of two-layered networks is strictly larger than the sum capacity of the two layers. The results obtained in this paper can serve as a guideline for the design of efficient multi-layered satellite networks.

In reality, pairwise interactions are no longer sufficient to describe the higher-order interactions between nodes, such as brain networks, social networks, etc., which often contain groups of three or more nodes. Since the failure of one node in a high-order network can lead to the failure of all simplices in which it is located and quickly propagates to the whole system through the interdependencies between networks, multilayered high-order interdependent networks are challenged with high vulnerability risks. To increase the robustness of higher-order networks, in this paper, we proposed a theoretical model of a two-layer partial high-order interdependent network, where a proportion of reinforced nodes are introduced that can function and support their simplices and components, even losing connection with the giant component. We study the order parameter of the proposed model, including the giant component and functional components containing at least one reinforced node, via theoretical analysis and simulations. Rich phase transition phenomena can be observed by varying the density of 2-simplices and the proportion of the network's reinforced nodes. Increasing the density of 2-simplices makes a double transition appear in the network. The proportion of reinforced nodes can alter the type of second transition of the network from discontinuous to continuous or transition-free, which is verified on the double random simplicial complex, double scale-free simplicial complex, and real-world datasets, indicating that reinforced nodes can significantly enhance the robustness of the network and can prevent networks from abrupt collapse. Therefore, the proposed model provides insights for designing robust interdependent infrastructure networks.

Pattern synchronization in a two-layer neuronal network is studied. For a single-layer network of Rulkov map neurons, there are three kinds of patterns induced by noise. Additive noise can induce ordered patterns at some intermediate noise intensities in a resonant way; however, for small and large noise intensities there exist excitable patterns and disordered patterns, respectively. For a neuronal network coupled by two single-layer networks with noise intensity differences between layers, we find that the two-layer network can achieve synchrony as the interlayer coupling strength increases. The synchronous states strongly depend on the interlayer coupling strength and the noise intensity difference between layers.

Synchronization effects for dissipative and inertial coupling between multiplex lattices

Complex networks in reality may suffer from target attacks which can trigger the breakdown of the entire network. It is therefore pivotal to evaluate the extent to which a network could withstand perturbations. The research on network robustness has proven as a potent instrument towards that purpose. The last two decades have witnessed the enthusiasm on the studies of network robustness. However, existing studies on network robustness mainly focus on multilayer networks while little attention is paid to multipartite networks which are an indispensable part of complex networks. In this study, we investigate the robustness of multipartite networks under intentional node attacks. We develop two network models based on the largest connected component theory to depict the cascading failures on multipartite networks under target attacks. We then investigate the robustness of computer‐generated multipartite networks with respect to eight node centrality metrics. We discover that the robustness of multipartite networks could display either discontinuous or continuous phase transitions. Interestingly, we discover that larger number of partite sets of a multipartite network could increase its robustness which is opposite to the phenomenon observed on multilayer networks. Our findings shed new lights on the robust structure design of complex systems. We finally present useful discussions on the applications of existing percolation theories that are well studied for network robustness analysis to multipartite networks. We show that existing percolation theories are not amenable to multipartite networks. Percolation on multipartite networks still deserves in‐depth efforts.

The consensus control problem of nonlinear cyber-physical systems with two-layer switching networks is investigated in this paper. Due to the hierarchical structure of two-layer networks, two-layer switching networks can simulate real networks more effectively than single-layer networks. In addition, the nonlinear component of the networks satisfies incremental quadratic constraints. An appropriate Lyapunov function is constructed to provide sufficient conditions for the node-to-node consensus problem. Furthermore, under some given assumptions and the node-to-node consensus, the complete consensus of two-layer networks is achieved. Finally, the validity of the method is verified by a simulation.

In the field of complex networks, understanding the spreading dynamics in multi-layer networks is crucial for real-world applications such as epidemic control and the analysis of social phenomenon. In this study, a two-layer interconnected network is established, with each layer modeled as a small-world network. To investigate the spreading dynamics on this two-layer network, the classic susceptible-infected-susceptible (SIS) model is applied to it. The governing equations for the Infection proportions on each layer are developed first, followed by the proof of the existence of steady solutions (the proportion of finally infected nodes in the network) and their analytical derivation. Then, the computational model is developed accurately track the time evolution of these solutions using the 4th-order Runge–Kutta method. Finally, a numerical investigation on the influence of parameters is carried out. Three categories of parameters are considered, including inter-layer parameters, intra-layer parameters, and recovery-related parameters. Their effects on the steady solution and the infection velocity of the SIS model on the two-layer networks are summarized. It is found that both inter-layer and intra-layer parameters significantly impact the infection dynamics, an increase in these parameters leads to an increase in the final Infection proportions and a decrease in the time to reach this state. For recovery-related parameters, there exists a maximum value due to the balance of contributions from different aspects. Besides, when the scales of the two layers are unequal, the influence of intra-layer parameters is more obvious for the layer with a smaller scale. The study may contribute to the understanding of spreading dynamics on multi-layer complex networks. It provides practical guidance for managing and controlling the spread of infections in real-world scenarios. The insights gained are valuable for related research and applications in areas like epidemiology and social network analysis.

We consider suppression of macroscopic synchronized oscillations in mixed populations of active and inactive oscillators with local diffusive coupling, described by a lattice complex Ginzburg-Landau model with discrete Laplacian in general dimensions. Approximate expression for the stability of the non-oscillatory stationary state is derived on the basis of the generalized free energy of the system. We show that an effective wavenumber of the system determined by the spatial arrangement of the active and inactive oscillators is an decisive factor in the suppression, in addition to the ratio of active population to inactive population and relative intensity of each population. The effectiveness of the proposed theory is illustrated with a cortico-thalamic model of epileptic seizures, where active and inactive oscillators correspond to epileptic foci and healthy cerebral cortex tissue, respectively.

Understanding the origin of valence band splitting is important because it governs the unique spin and valley physics in few-layer MoS2. We explore the effects of spin-orbit coupling and interlayer coupling on few-layer MoS2 using first-principles methods. We find spin-orbit coupling has a major contribution to the valence band splitting at K in multilayer MoS2. In double-layer MoS2, the interlayer coupling leads to the widening of the gap between the already spin-orbit split states. This is also the case for the bands of the K-point in bulk MoS2. In triple-layer MoS2, the strength of interlayer coupling of the spin-up channel becomes different from that of spin-down at K. This combined with spin-orbit coupling results in the band splitting in two main valence bands at K. With the increase of pressure, this phenomenon becomes more obvious with a decrease of main energy gap in the splitting valence bands at the K valley.

Using network ecology to understand and mitigate long‐term insect declines

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

Most work on convention propagation have focused on single-layer networks. This work a) highlights the need for studying convention propagation in multi-layer networks, b) presents results comparing the speed of convention propagation in single-layer vs. multi-layer networks and c) demonstrates the role of influencer agents in convention propagation in multi-layer networks.

This work investigates the synchronization problems of a two-layered network, where the involved nodes are of delay nonlinearity. By using a generalized delay differential inequality, some sufficient conditions are established for reaching synchronization between the two layers. It is revealed that when the inter-layer coupling strength is time-varying, the time average of the smallest eigenvalue of an induced matrix plays a key role in reaching synchronization. Meanwhile, the largest admissible delay is also estimated. Numerical examples are also given to demonstrate the validity of the theoretical results.