Related papers: Infinitesimal Homeostasis in Mass-Action Systems
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…
New checkable criteria for persistence of chemical reaction networks are proposed, which extend and complement those obtained by the authors in previous work. The new results allow the consideration of reaction rates which are time-varying,…
We consider the question whether a chemical reaction network preserves the number and stability of its positive steady states upon inclusion of inflow and outflow reactions. Often a model of a reaction network is presented without inflows…
Persistence and permanence are properties of dynamical systems that describe the long-term behavior of the solutions, and in particular specify whether positive solutions approach the boundary of the positive orthant. Mass-action systems…
Biochemical processes typically involve many chemical species, some in abundance and some in low molecule numbers. Here we first identify the rate constant limits under which the concentrations of a given set of species will tend to…
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…
At the microscopic scale, open chemical reaction networks are described by stochastic reactions that follow mass-action kinetics and are coupled to chemostats. We show that closed chemical reaction networks -- with specific stoichiometries…
We propose a principle of consistency between different hierarchical levels of biological systems. Given a consistency between molecule replication and cell reproduction, universal statistical laws on cellular chemical abundances are…
Stochastic chemical reaction or population dynamics in finite systems often terminates in an absorbing state. Yet in large spatially extended systems, the time to reach species extinction (or fixation) becomes exceedingly long. Tuning…
We consider chemical reaction networks taken with mass action kinetics. The steady states of such a system are solutions to a system of polynomial equations. Even for small systems the task of finding the solutions is daunting. We develop…
Controlling complex reaction networks is a fundamental challenge in the fields of physics, biology, and systems engineering. Here, we prove a general principle for catalytic reaction systems with kinetics where the reaction order and the…
A binary fluid mixture in contact with lateral particle reservoirs is considered. By imposing different particle concentrations in these reservoirs, the system can be maintained under controlled non-equilibrium conditions. Previous…
Stochastic chemical processes are described by the chemical master equation satisfying the law of mass-action. We first ask whether the dual master equation, which has the same steady state as the chemical master equation, but with inverted…
Biochemical models that exhibit bistability are of interest to biologists and mathematicians alike. Chemical reaction network theory can provide sufficient conditions for the existence of bistability, and on the other hand can rule out the…
The problem of finite-dimensional asymptotics of infinite-dimensional dynamic systems is studied. A non-linear kinetic system with conservation of supports for distributions has generically finite-dimensional asymptotics. Such systems are…
Many of the chemical reactions that take place within a living cell are irreversible. Due to evolutionary pressures, the number of allowable reactions within these systems are highly constrained and thus the resulting metabolic networks…
The detailed balance property is a fundamental property that must be satisfied in all the macroscopic systems with a well defined temperature at each point. On the other hand, many biochemical networks work in non-equilibrium conditions and…
We study a stochastic two-species chemical reaction system with two mechanisms. One mechanism consists of chemical interactions which govern the overall drift of species amounts in the system; the other mechanism consists of resampling,…
Biomolecular processes are typically modeled using chemical reaction networks coupled to infinitely large chemical reservoirs. A difference in chemical potential between these reservoirs can drive the system into a non-equilibrium steady…
The paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand,…