相关论文: Nonlinear consensus on networks: equilibria, effec…

We study a non-linear dynamical system on networks inspired by the pitchfork bifurcation normal form. The system has several interesting interpretations: as an interconnection of several pitchfork systems, a gradient dynamical system and…

This work considers the robustness of uncertain consensus networks. The first set of results studies the stability properties of consensus networks with negative edge weights. We show that if either the negative weight edges form a cut in…

We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…

The purpose of this short paper is to provide a theoretical analysis for the consensus problem under nonlinear protocols. A main contribution of this work is to generalize the previous consensus problems under nonlinear protocols for…

In this paper, we study a class of equations representing nonlinear diffusion on networks. A particular instance of our model can be seen as a network equivalent of the porous-medium equation. We are interested in studying perturbations of…

Consensus over networked agents is typically studied using undirected or directed communication graphs. Undirected graphs enforce symmetry in information exchange, leading to convergence to the average of initial states, while directed…

We study distributed computation in synchronous dynamic networks where an omniscient adversary controls the unidirectional communication links. Its behavior is modeled as a sequence of directed graphs representing the active (i.e. timely)…

To any inhibition-dominated threshold-linear network (TLN) we can associate a directed graph that captures the pattern of strong and weak inhibition between neurons. Robust motifs are graphs for which the structure of fixed points in the…

The basic interaction unit of many dynamical systems involves more than two nodes. In such situations where networks are not an appropriate modelling framework, it has recently become increasingly popular to turn to higher-order models,…

The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…

In this paper, we provide a theoretical analysis for nonlinear discontinuous consensus protocols in networks of multiagents over weighted directed graphs. By integrating the analytic tools from nonsmooth stability analysis and graph theory,…

In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically,…

Coupled oscillator networks show a complex interrelations between topological characteristics of the network and the nonlinear stability of single nodes with respect to large but realistic perturbations. We extend previous results on these…

We analyse a collection of empirical networks in a wide spectrum of disciplines and show that strong non-normality is ubiquitous in network science. Dynamical processes evolving on non-normal networks exhibit a peculiar behaviour, as…

This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence…

The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle…

We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…

There has been substantial work studying consensus problems for which there is a single common final state, although there are many real-world complex networks for which the complete consensus may be undesirable. More recently, the concept…

We study the stability of the dynamics of a network of n neurons intercting linearly through a random gaussian matrix of excitatory and inhibitory type. Using the aproach developed in a previous paper we show some interesting properties of…

Modularity structures are common in various social and biological networks. However, its dynamical origin remains an open question. In this work, we set up a dynamical model describing the evolution of a social network. Based on the…