Related papers: Extinction in Reaction Network Models
State convergence is essential in several scientific areas, e.g. multi-agent consensus/disagreement, distributed optimization, monotone game theory, multi-agent learning over time-varying networks. This paper is the first on state…
Stochastic reaction networks are dynamical models of biochemical reaction systems and form a particular class of continuous-time Markov chains on $\mathbb{N}^n$. Here we provide a fundamental characterisation that connects structural…
We propose a novel network growth model coupled with the competition interaction to simulate macroevolution. Our work shows that the competition plays an important role in macroevolution and it is more rational to describe the interaction…
We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded…
There is empirical evidence from a range of disciplines that as the connectivity of a network increases, we observe an increase in the average fitness of the system. But at the same time, there is an increase in the proportion of…
We analyze the input-output behavior of residual networks from a dynamical system point of view by disentangling the residual dynamics from the output activities before the classification stage. For a network with simple skip connections…
Large time dynamics of reaction-diffusion systems modeling some irreversible reaction networks are investigated. Depending on initial masses, these networks possibly possess boundary equilibria, where some of the chemical concentrations are…
We study the Lyapunov exponents of models that are close to skew product systems over a C__ uniformly expanding transformation of the circle. For a continuous fibre map $\phi$, analytic, increasing, and convex in the fibre variable, we…
Understanding the mechanisms governing population extinctions is of key importance to many problems in ecology and evolution. Stochastic factors are known to play a central role in extinction, but the interactions between a population's…
We study species abundance in the empirical plant-pollinator mutualistic networks exhibiting broad degree distributions, with uniform intra-group competition assumed, by the Lotka-Volterra equation. The stability of a fixed point is found…
Zero-one biochemical reaction networks are widely recognized for their importance in analyzing signal transduction and cellular decision-making processes. Degenerate networks reveal non-standard behaviors and mark the boundary where…
This work investigates how biodiversity is affected in a cyclic spatial May-Leonard model with hierarchical and non-hierarchical rules. Here we propose a generalization of the traditional rock-paper-scissors model by considering highly…
In this paper, the extinction problem for a class of distylous plant populations is considered within the framework of certain nonhomogeneous nearest-neighbor random walks in the positive quadrant. For the latter, extinction means…
A natural condition on the structure of the underlying chemical reaction network, namely weak reversibility, is shown to guarantee the existence of an equilibrium (steady state) in each positive stoichiometric compatibility class for the…
We study a generic reaction-diffusion model for single-species population dynamics that includes reproduction, death, and competition. The population is assumed to be confined in a refuge beyond which conditions are so harsh that they lead…
Stochastic reaction networks with mass-action kinetics provide a useful framework for understanding processes -- biochemical and otherwise -- in homogeneous environments. However, cellular reactions are often compartmentalized, either at…
We consider steady states of dynamics that have an underlying network structure. We study how a steady state responds to small perturbations in the network parameters and how this sensitivity is connected to the network structure. We…
How self-organized networks develop, mature and degenerate is a key question for sociotechnical, cyberphysical and biological systems with potential applications from tackling violent extremism through to neurological diseases. So far, it…
Acquiring fear responses to predictors of aversive outcomes is crucial for survival. At the same time, it is important to be able to modify such associations when they are maladaptive, for instance in treating anxiety and trauma-related…
A class of distributed systems with a cyclic interconnection structure is considered. These systems arise in several biochemical applications and they can undergo diffusion driven instability which leads to a formation of spatially…