Related papers: Extinction in Reaction Network Models
In the study of reaction networks and the polynomial dynamical systems that they generate, special classes of networks with important properties have been identified. These include reversible, weakly reversible}, and, more recently,…
Reaction networks are mathematical models of interacting chemical species that are primarily used in biochemistry. There are two modeling regimes that are typically used, one of which is deterministic and one that is stochastic. In…
The extinction of species is a major problem of concern with a large literature. Our investigation gives insight into when species extinctions must occur, with an emphasis on determining which species might possibly die out and on how fast…
We study a model of a multi-species ecosystem described by Lotka-Volterra-like equations. Interactions among species form a network whose evolution is determined by the dynamics of the model. Numerical simulations show power-law…
We study the stability of $\mathcal{M}_0$, an invariant subset of a Markov process $(X_t)_{t\geq 0}$ on a metric space $\mathcal{M}$. By building the theory of average Lyapunov functions, we formulate general criteria based on the signs of…
Extinction of an epidemic or a species is a rare event that occurs due to a large, rare stochastic fluctuation. Although the extinction process is dynamically unstable, it follows an optimal path that maximizes the probability of…
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,…
We study chemical reaction networks with discrete state spaces, such as the standard continuous time Markov chain model, and present sufficient conditions on the structure of the network that guarantee the system exhibits an extinction…
Recent work of M.D. Johnston et al. has produced sufficient conditions on the structure of a chemical reaction network which guarantee that the corresponding discrete state space system exhibits an extinction event. The conditions consist…
We consider linear elimination of variables in steady state equations of a chemical reaction network. Particular subsets of variables corresponding to sets of so-called reactant-noninteracting species, are introduced. The steady state…
Reaction networks can display a wide array of dynamics. However, it is possible for different reaction networks to display the same dynamics. This phenomenon is called dynamical equivalence and makes network identification a hard problem to…
A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as…
We consider the relationship between stationary distributions for stochastic models of reaction systems and Lyapunov functions for their deterministic counterparts. Specifically, we derive the well known Lyapunov function of reaction…
We consider the problem of extinction processes on random networks with a given structure. For sufficiently large well-mixed populations, the process of extinction of one or more state variable components occurs in the tail of the…
An important dynamical property of biological interaction networks is persistence, which intuitively means that "no species goes extinct". It has been conjectured that dynamical system models of weakly reversible networks (i.e., networks…
A class of chemical reaction networks is described with the property that each positive equilibrium is locally asymptotically stable relative to its stoichiometry class, an invariant subspace on which it lies. The reaction systems treated…
We establish weak-strong uniqueness and stability properties of renormalised solutions to a class of energy-reaction-diffusion systems. The systems considered are motivated by thermodynamically consistent models, and their formal entropy…
We introduce the notion of non-oscillation, propose a constructive method for its robust verification, and study its application to biological interaction networks (also known as, chemical reaction networks). We begin by revisiting…
We study stochastic extinction for a class of Markov processes motivated by models in ecology and epidemiology. Extinction is often characterized by a boundedness condition and a condition on boundary Lyapunov exponents (invasion rates).…
In this paper, the dynamics of a phytoplankton-zooplankton system with linear functional responses are examined. For the continuous-time model, the global asymptotic stability of the fixed points is demonstrated by constructing Lyapunov…