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Well-mixed chemical reaction networks (CRNs) contain many distinct chemical species with copy numbers that fluctuate in correlated ways. While those correlations are typically monitored via Monte Carlo sampling of stochastic trajectories,…
In this paper we study the performance of a bipartite network in which customers arrive at the nodes of the network, but not all nodes are able to serve their customers at all times. Each node can be either active or inactive, and two nodes…
It has recently been shown that structural conditions on the reaction network, rather than a 'fine-tuning' of system parameters, often suffice to impart 'absolute concentration robustness' on a wide class of biologically relevant,…
The seemingly stochastic transient dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference. In vitro neurons, on the other hand, exhibit a highly deterministic…
We study an excitable active rotator with slowly adapting nonlinear feedback and noise. Depending on the adaptation and the noise level, this system may display noise-induced spiking, noise-perturbed oscillations, or stochastic busting. We…
Reaction networks are widely used models to describe biochemical processes. Stochastic fluctuations in the counts of biological macromolecules have amplified consequences due to their small population sizes. This makes it necessary to favor…
We introduce a simple model of static networks, where nodes are located on a ring structure, and two accompanying dynamic rules of repeated averaging on periodic node states. We assume nodes can interact with neighbors, and will add…
The structure and dynamic of social network are largely determined by the heterogeneous interaction activity and social capital allocation of individuals. These features interplay in a non-trivial way in the formation of network and…
We present a simple Markov model of spiking neural dynamics that can be analytically solved to characterize the stochastic dynamics of a finite-size spiking neural network. We give closed-form estimates for the equilibrium distribution,…
Biological networks have been recently found to exhibit many topological properties of the so-called complex networks. It has been reported that they are, in general, both highly skewed and directed. In this paper, we report on the dynamics…
We study transient sequential dynamics of evolving dynamical networks, i.e., those having active nodes and links and activity-dependent topology. We show that such networks can generate sequences of metastable cluster states where each…
We study the stochastic dynamics of strongly-coupled excitable elements on a tree network. The peripheral nodes receive independent random inputs which may induce large spiking events propagating through the branches of the tree and leading…
Steady states are frequently used to investigate the long-term behaviors of (bio)-chemical systems. Recently, there has been a growing interest in network-based approaches due to their efficiency in deriving parametrizations of positive…
We consider the coaction of two distinct noise sources on the activation process of a single and two interacting excitable units, which are mathematically described by the Fitzhugh-Nagumo equations. We determine the most probable activation…
We give a constructive method for realizing an arbitrary directed graph (with no one-cycles) as a heteroclinic or an excitable dynamic network in the phase space of a system of coupled cells of two types. In each case, the system is…
The paper examines the discrete-time dynamics of neuron models (of excitatory and inhibitory types) with piecewise linear activation functions, which are connected in a network. The properties of a pair of neurons (one excitatory and the…
This paper analyzes stochastic networks consisting of a set of finite capacity sites where different classes of individuals move according to some routing policy. The associated Markov jump processes are analyzed under a thermodynamic limit…
For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is…
In this paper, we consider stable stochastic linear systems modeling whole-brain resting-state dynamics. We parametrize the state matrix of the system (effective connectivity) in terms of its steady-state covariance matrix (functional…
We present a mathematical description of the voter model dynamics on heterogeneous networks. When the average degree of the graph is $\mu \leq 2$ the system reaches complete order exponentially fast. For $\mu >2$, a finite system falls,…