Related papers: First order endotactic reaction networks
Reaction networks have been widely used as generic models in diverse areas of applied sciences, such as biology, chemistry, ecology, epidemiology, and computer science. A reaction network incorporating noisy effects is modeled as a…
Delay mass-action systems provide a model of chemical kinetics when past states influence the current dynamics. In this work, we provide a graph-theoretic condition for delay stability, i.e., linear stability independent of both rate…
Chemical reaction networks are a widely accepted modeling framework for diverse science phenomena stemming from all disciplines of science, such as biochemistry, ecology, epidemiology, social and political science. In this paper we prove…
Reaction networks are mainly used to model the time-evolution of molecules of interacting chemical species. Stochastic models are typically used when the counts of the molecules are low, whereas deterministic models are used when the counts…
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 introduce a unifying and generalizing framework for complex and detailed balanced steady states in chemical reaction network theory. To this end, we generalize the graph commonly used to represent a reaction network. Specifically, we…
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…
The quasi-steady state approximation and time-scale separation are commonly applied methods to simplify models of biochemical reaction networks based on ordinary differential equations (ODEs). The concentrations of the "fast" species are…
In this paper, we propose a novel technique, referred to as the Lyapunov Function PDEs technique, to diagnose persistence of chemical reaction networks with mass-action kinetics. The technique allows that every network is attached to a…
Motivated by recent progress on the interplay between graph theory, dynamics, and systems theory, we revisit the analysis of chemical reaction networks described by mass action kinetics. For reaction networks possessing a thermodynamic…
Stochastic reaction networks (SRNs) provide models of many real-world networks. Examples include networks in epidemiology, pharmacology, genetics, ecology, chemistry, and social sciences. Here, we model stochastic reaction networks by…
We establish a new relationship between monotonicity and contractivity and use this connection to describe a new general class of weakly contractive reaction networks. The new class is characterized by the stoichiometry matrix of the…
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…
In a recent paper it was shown that, for chemical reaction networks possessing a subtle structural property called concordance, dynamical behavior of a very circumscribed (and largely stable) kind is enforced, so long as the kinetics lies…
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,…
Biochemical reaction networks are widely applied across scientific disciplines to model complex dynamic systems. We investigate the diffusion approximation of reaction networks with mass-action kinetics, focusing on the identifiability of…
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 show that there exists endotactic and strongly endotactic dynamical systems that are not weakly reversible and possess infinitely many steady states. We provide a few examples in two dimensions and an example in three dimensions that…
Many biochemical and industrial applications involve complicated networks of simultaneously occurring chemical reactions. Under the assumption of mass action kinetics, the dynamics of these chemical reaction networks are governed by systems…
We study a system of reaction-diffusion equations posed on a bounded domain composed of subdomains separated by a connected network with a metric graph structure. The reaction-diffusion dynamics with anisotropic diffusion on the graph edges…