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A dynamical system obtains a wide variety of kinetic realizations, which is advantageous for the analysis of biochemical systems. A reaction network, derived from a dynamical system, may or may not possess some properties needed for a…

Molecular Networks · Quantitative Biology 2024-05-01 Dylan Antonio Talabis , Eduardo Mendoza

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. The original problem…

Dynamical Systems · Mathematics 2011-07-05 Gabor Szederkenyi , Katalin M. Hangos , Zsolt Tuza

The behavior of dynamical system interacting with non-equilibrium medium is investigated. Formally exact kinetic equations are derived for the statistical operator of the dynamical system and the macroscopic parameters of the medium. In the…

Statistical Mechanics · Physics 2016-12-30 Mikheil Zviadadze , Alexander kvirikadze

Reaction systems are discrete dynamical systems inspired by bio-chemical processes, whose dynamical behaviour is expressed by set-theoretic operations on finite sets. Reaction systems thus provide a description of bio-chemical phenomena…

Formal Languages and Automata Theory · Computer Science 2020-08-05 Alberto Dennunzio , Enrico Formenti , Luca Manzoni , Antonio E. Porreca

An inverse problem framework for constructing reaction systems with prescribed properties is presented. Kinetic transformations are defined and analysed as a part of the framework, allowing an arbitrary polynomial ordinary differential…

Dynamical Systems · Mathematics 2015-10-27 Tomislav Plesa , Tomas Vejchodsky , Radek Erban

The analysis of observable phenomena (for instance, in biology or physics) allows the detection of dynamical behaviors and, conversely, starting from a desired behavior allows the design of objects exhibiting that behavior in engineering.…

Discrete Mathematics · Computer Science 2026-04-10 Antonio E. Porreca , Marius Rolland

Chemical reaction networks in living cells maintain precise control over thousands of metabolites despite operating far from equilibrium under constant perturbations. While mass action kinetics accurately describe the underlying dynamics,…

Optimization and Control · Mathematics 2025-08-27 Steven Diamond

Motivation: A Chemical Reaction Network (CRN) is a set of chemical reactions, which can be very complex and difficult to analyze. Indeed, dynamical properties of CRNs can be described by a set of non-linear differential equations that…

Computational Engineering, Finance, and Science · Computer Science 2021-07-02 Lucia Nasti , Roberta Gori , Paolo Milazzo , Federico Poloni

Much attention has been focused in recent years on the following algebraic problem arising from applications: which chemical reaction networks, when taken with mass-action kinetics, admit multiple positive steady states? The interest behind…

Dynamical Systems · Mathematics 2018-06-06 Anne Shiu , Timo de Wolff

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…

Dynamical Systems · Mathematics 2014-07-15 Matthew D. Johnston

A crisp survey is given of chemical reaction networks from the perspective of general nonlinear network dynamics, in particular of consensus dynamics. It is shown how by starting from the complex-balanced assumption the reaction dynamics…

Dynamical Systems · Mathematics 2015-02-10 Arjan van der Schaft , Shodhan Rao , Bayu Jayawardhana

The goal of this paper is to gather and develop some necessary and sufficient criteria for injectivity and multistationarity in vector fields associated with a chemical reaction network under a variety of more or less general assumptions on…

Dynamical Systems · Mathematics 2016-10-28 Murad Banaji , Casian Pantea

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…

Dynamical Systems · Mathematics 2022-05-03 Abhishek Deshpande

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…

Quantitative Methods · Quantitative Biology 2011-11-14 Jian Deng , Christopher Jones , Martin Feinberg , Adrian Nachman

Mass-action chemical reaction systems are frequently used in Computational Biology. The corresponding polynomial dynamical systems are often large (consisting of tens or even hundreds of ordinary differential equations) and poorly…

Dynamical Systems · Mathematics 2011-07-13 Mercedes Perez Millan , Alicia Dickenstein , Anne Shiu , Carsten Conradi

This work addresses multistationarity of fully open reaction networks equipped with mass action kinetics. We improve upon the existing results relating existence of positive feedback loops in a reaction network and multistationarity; and we…

Molecular Networks · Quantitative Biology 2025-11-11 Shenghao Yao , AmirHosein Sadeghimanesh , Matthew England

Chemical reaction networks describe interactions between biochemical species. Once an underlying reaction network is given for a biochemical system, the system dynamics can be modelled with various mathematical frameworks such as continuous…

Probability · Mathematics 2023-06-22 German Enciso , Radek Erban , Jinsu Kim

Given a dynamical system with polynomial right-hand side, can it be generated by a reaction network that possesses certain properties? This question is important because some network properties may guarantee specific dynamical properties,…

Dynamical Systems · Mathematics 2023-03-17 Gheorghe Craciun , Abhishek Deshpande , Jiaxin Jin

Living systems are forced away from thermodynamic equilibrium by exchange of mass and energy with their environment. In order to model a biochemical reaction network in a non-equilibrium state one requires a mathematical formulation to…

Molecular Networks · Quantitative Biology 2012-02-21 Ronan M. T. Fleming , Ines Thiele

Biochemical networks are used in computational biology, to model the static and dynamical details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as…

Molecular Networks · Quantitative Biology 2014-10-15 Ovidiu Radulescu , Alexander N. Gorban , Andrei Zinovyev , Vincent Noel