Related papers: Characterizing short-term stability for Boolean ne…

Stability is an important characteristic of network models that has implications for other desirable aspects such as controllability. The stability of a Boolean network depends on various factors, such as the topology of its wiring diagram…

We performed a numerical study on random Boolean networks with power-law rank outdegree distributions to find local structural cause for the emergence of high or low degree of coherence in binary state variables. The degree of randomness…

We study two measures of the complexity of heterogeneous extended systems, taking random Boolean networks as prototypical cases. A measure defined by Shalizi et al. for cellular automata, based on a criterion for optimal statistical…

The spread of viruses in biological networks, computer networks, and human contact networks can have devastating effects; developing and analyzing mathematical models of these systems can be insightful and lead to societal benefits. Prior…

Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…

Boolean networks serve as discrete models of regulation and signaling in biological cells. Identifying the key controllers of such processes is important for understanding the dynamical systems and planning further analysis. Here we…

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…

In this paper, we address the stability of transport systems and wave propagation on networks with time-varying parameters. We do so by reformulating these systems as non-autonomous difference equations and by providing a suitable…

With a simple model, we study the evolution of random networks under attack and reconstruction. We introduce a new quality, invulnerability I(s), to describe the stability of the system. We find that the network can evolve to a stationary…

Many biological systems, such as metabolic pathways, exhibit bistability behavior: these biological systems exhibit two distinct stable states with switching between the two stable states controlled by certain conditions. Since…

We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU…

Spreading on networks is influenced by a number of factors including different parts of the inter-event time distribution (IETD), the topology of the network and non-stationarity. In order to understand the role of these factors we study…

We discuss the analysis and stability of a family of cross-diffusion boundary value problems with nonlinear diffusion and drift terms. We assume that these systems are close, in a suitable sense, to a set of decoupled and linear problems.…

We consider the problem of solving consensus using deterministic algorithms in a synchronous dynamic network with unreliable, directional point-to-point links, which are under the control of a message adversary. In contrast to a large body…

Networks in nature do not act in isolation but instead exchange information, and depend on each other to function properly. An incipient theory of Networks of Networks have shown that connected random networks may very easily result in…

Swarm stability is concerned for descriptor compartmental networks with linear time-invariant protocol. Compartmental network is a specific type of dynamical multi-agent system. Necessary and sufficient conditions for both consensus and…

We discuss how spreading processes on temporal networks are impacted by the shape of their inter-event time distributions. Through simple mathematical arguments and toy examples, we find that the key factor is the ordering in which events…

We study spreading on networks where the contact dynamics between the nodes is governed by a random process and where the inter-contact time distribution may differ from the exponential. We consider a process of imperfect spreading, where…

Random boolean networks are a model of genetic regulatory networks that has proven able to describe experimental data in biology. They not only reproduce important phenomena in cell dynamics, but they are also extremely interesting from a…

Time evolution of diluted neural networks with a nonmonotonic transfer function is analitically described by flow equations for macroscopic variables. The macroscopic dynamics shows a rich variety of behaviours: fixed-point, periodicity and…