相关论文: Realizations of kinetic differential equations

A method to calculate reactions in quantum mechanics is outlined. It is advantageous, in particular, in problems with many open channels of various nature i.e. when energy is not low. In the method there is no need to specify reaction…

This paper is concerned with the dynamical properties of deterministically modeled chemical reaction systems with mass-action kinetics. Such models are ubiquitously found in chemistry, population biology, and the burgeoning field of systems…

The role of differential equations in the process of calculating Feynman integrals is reviewed. An example of a diagram is given for which the method of differential equations was introduced, the properties of the inverse-mass-expansion…

The automated inference of physically interpretable (bio)chemical reaction network models from measured experimental data is a challenging problem whose solution has significant commercial and academic ramifications. It is demonstrated,…

Universal intermittent dynamics in a random catalytic reaction network, induced by smallness in the molecule number is reported. Stochastic simulations for a random catalytic reaction network subject to a flow of chemicals show that the…

Engineering molecular systems that exhibit complex behavior requires the design of kinetic barriers. For example, an effective catalytic pathway must have a large barrier when the catalyst is absent. While programming such energy barriers…

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…

An algorithm is given in this paper for the computation of dynamically equivalent weakly reversible realizations with the maximal number of reactions, for chemical reaction networks (CRNs) with mass action kinetics.

Chemical reaction networks with generalized mass-action kinetics lead to power-law dynamical systems. As a simple example, we consider the Lotka reactions with two chemical species and arbitrary power-law kinetics. We study existence,…

Machine learning techniques applied to chemical reactions has a long history. The present contribution discusses applications ranging from small molecule reaction dynamics to platforms for reaction planning. ML-based techniques can be of…

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…

Bistability and multistationarity are properties of reaction networks linked to switch-like responses and connected to cell memory and cell decision making. Determining whether and when a network exhibits bistability is a hard and open…

Complex networks, comprised of individual elements that interact with each other through reaction channels, are ubiquitous across many scientific and engineering disciplines. Examples include biochemical, pharmacokinetic, epidemiological,…

This paper presents an algebraic framework to study sign-sensitivities for reaction networks modeled by means of systems of ordinary differential equations. Specifically, we study the sign of the derivative of the concentrations of the…

The general theory of a complex system of nonlinear chemical reactions is a primary language of chemistry that includes chemical engineering and cellular biochemistry. Its significance as an analytical framework, however, has not been fully…

Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential…

This paper studies the relations among system parameters, uniqueness, and stability of equilibria, for kinetic systems given in the form of polynomial ODEs. Such models are commonly used to describe the dynamics of nonnegative systems, with…

Reaction networks taken with mass-action kinetics arise in many settings, from epidemiology to population biology to systems of chemical reactions. Bistable reaction networks are posited to underlie biochemical switches, which motivates the…

A computation-oriented representation of uncertain kinetic systems is introduced and analysed in this paper. It is assumed that the monomial coefficients of the ODEs belong to a polytopic set, which defines a set of dynamical systems for an…

Differentiable quantum dynamics require automatic differentiation of a complex-valued initial value problem, which numerically integrates a system of ordinary differential equations from a specified initial condition, as well as the…