Related papers: Stability of Boolean Multilevel Networks
Multilayer networks describe well many real interconnected communication and transportation systems, ranging from computer networks to multimodal mobility infrastructures. Here, we introduce a model in which the nodes have a limited…
We examine analytically the existence and stability of phase-locked states in a weakly heterogeneous neuronal network. We consider a model of N neurons with all-to-all synaptic coupling where the heterogeneity is in the firing frequency or…
We study the stationary states of networks consisting of weakly coupled bistable units. We prove the existence of a high multiplicity of stable steady states in networks with very general inter-unit dynamics. We present a method for…
We study synchronization dynamics in networks of coupled oscillators with bimodal distribution of natural frequencies. This setup can be interpreted as a simple model of frequency synchronization dynamics among generators and loads working…
Synchronization phenomena are of broad interest across disciplines and increasingly of interest in a multiplex network setting. Here we show how the Master Stability Function, a celebrated framework for analyzing synchronization on a single…
We investigate the collective dynamics of bi-stable elements connected in different network topologies, ranging from rings and small-world networks, to scale-free networks and stars. We estimate the dynamical robustness of such networks by…
Many natural, engineered, and social systems can be represented using the framework of a layered network, where each layer captures a different type of interaction between the same set of nodes. The study of such multiplex networks is a…
Knowledge graphs play a central role for linking different data which leads to multiple layers. Thus, they are widely used in big data integration, especially for connecting data from different domains. Few studies have investigated the…
We present a linear stability analysis of stationary states (or fixed points) in large dynamical systems defined on random directed graphs with a prescribed distribution of indegrees and outdegrees. We obtain two remarkable results for such…
Real-world systems in epidemiology, social sciences, power transportation, economics and engineering are often described as multilayer networks. Here we first define and compute the symmetries of multilayer networks, and then study the…
In this paper, we consider the stability analysis of large-scale distributed networked control systems with random communication delays between linearly interconnected subsystems. The stability analysis is performed in the Markov jump…
The aim of this paper is to rigorously study dynamics of Heterogeneously Coupled Maps (HCM). Such systems are determined by a network with heterogeneous degrees. Some nodes, called hubs, are very well connected while most nodes interact…
In this paper we investigate equilibria of continuous differential equation models of network dynamics. The motivation comes from gene regulatory networks where each directed edge represents either down- or up-regulation, and is modeled by…
From critical infrastructure, to physiology and the human brain, complex systems rarely occur in isolation. Instead, the functioning of nodes in one system often promotes or suppresses the functioning of nodes in another. Despite advances…
Continuous-time systems with switch-like behaviour occur in chemical kinetics, gene regulatory networks and neural networks. Networks with hard switching, as a limiting case of smooth sigmoidal switching, retain the richest possible range…
Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider…
We realize autonomous Boolean networks by using logic gates in their autonomous mode-of-operation on a field-programmable gate array. This allows us to implement time-continuous systems with complex dynamical behaviors that can be…
Regulatory dynamics in biology is often described by continuous rate equations for continuously varying chemical concentrations. Binary discretization of state space and time leads to Boolean dynamics. In the latter, the dynamics has been…
This paper investigates the stabilization of probabilistic Boolean networks (PBNs) via a novel pinning control strategy based on network structure. In a PBN, the evolution equation of each gene switches among a collection of candidate…
We explore the relation between the topological relevance of a node in a complex network and the individual dynamics it exhibits. When the system is weakly coupled, the effect of the coupling strength against the dynamical complexity of the…