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A chemical reaction network (CRN) is composed of reactions that can be seen as interactions among entities called species, which exist within the system. Endowed with kinetics, CRN has a corresponding set of ordinary differential equations…

Dynamical Systems · Mathematics 2021-04-20 Bryan S. Hernandez , Ralph John L. De la Cruz

Chemical reaction networks (CRNs) formally model chemistry in a well-mixed solution. CRNs are widely used to describe information processing occurring in natural cellular regulatory networks, and with upcoming advances in synthetic biology,…

Computational Complexity · Computer Science 2013-04-17 David Doty

Understanding the emergent behavior of chemical reaction networks (CRNs) is a fundamental aspect of biology and its origin from inanimate matter. A closed CRN monotonically tends to thermal equilibrium, but when it is opened to external…

Molecular Networks · Quantitative Biology 2024-05-16 Masanari Shimada , Pegah Behrad , Eric De Giuli

Across many disciplines, chemical reaction networks (CRNs) are an established population model defined as a system of coupled nonlinear ordinary differential equations. In many applications, for example, in systems biology and epidemiology,…

Systems and Control · Electrical Eng. & Systems 2023-01-23 Kim G. Larsen , Daniele Toller , Mirco Tribastone , Max Tschaikowski , Andrea Vandin

Chemical reaction networks (CRNs) provide a convenient language for modelling a broad variety of biological systems. These models are commonly studied with respect to the time series they generate in deterministic or stochastic simulations.…

Molecular Networks · Quantitative Biology 2019-07-11 Ozan Kahramanoğulları

Both natural and synthetic chemical systems not only exhibit a range of non-trivial dynamics, but also transition between qualitatively different dynamical behaviours as environmental parameters change. Such transitions are called…

Molecular Networks · Quantitative Biology 2026-02-03 Alexander Dack , Tomislav Plesa , Thomas E. Ouldridge

We show that if a chemical reaction network (CRN) admits nondegenerate (resp., linearly stable) oscillation, and we add new reversible reactions involving new species to this CRN, then the new CRN so created also admits nondegenerate…

Dynamical Systems · Mathematics 2021-06-14 Murad Banaji

The Hilbert number $H(n)$ is defined as the maximum number of limit cycles of a planar autonomous system of ordinary differential equations (ODEs) with right-hand sides containing polynomials of degree at most $n \in {\mathbb N}$. The…

Dynamical Systems · Mathematics 2025-04-22 Gheorghe Craciun , Radek Erban

Formal methods have enabled breakthroughs in many fields, such as in hardware verification, machine learning and biological systems. The key object of interest in systems biology, synthetic biology, and molecular programming is chemical…

Emerging Technologies · Computer Science 2020-08-11 Marko Vasic , David Soloveichik , Sarfraz Khurshid

Some results are presented on how oscillation is inherited by chemical reaction networks (CRNs) when they are built in natural ways from smaller oscillatory networks. The main results describe four important ways in which a CRN can be…

Dynamical Systems · Mathematics 2017-11-07 Murad Banaji

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

We show that adding new chemical species into the reactions of a chemical reaction network (CRN) in such a way that the rank of the network remains unchanged preserves its capacity for multiple nondegenerate equilibria and/or periodic…

Dynamical Systems · Mathematics 2022-09-14 Murad Banaji , Balázs Boros , Josef Hofbauer

We address a fundamental question: under which conditions do the dynamics and thermodynamics of open chemical reaction networks (CRNs), grounded on the notion of idealized chemostats that exchange selected species, emerge from underlying…

Statistical Mechanics · Physics 2026-04-17 Benedikt Remlein , Massimiliano Esposito , Francesco Avanzini

Living systems operate out of equilibrium, continuously consuming energy to sustain organised, functional states. Their emergent behaviour usually relies on a set of interconnected chemical reaction networks (CRNs) driven by external fluxes…

Statistical Mechanics · Physics 2026-02-03 Shiling Liang , Paolo De Los Rios , Daniel Maria Busiello

The thermodynamic and dynamical conditions necessary to observe indefinite growth in homogeneous open chemical reaction networks (CRNs) satisfying mass action kinetics were presented in Srinivas et al. (2023): Unimolecular CRNs can only…

Molecular Networks · Quantitative Biology 2024-12-05 Shesha Gopal Marehalli Srinivas , Francesco Avanzini , Massimiliano Esposito

Stochastic chemical reaction networks (CRNs) are complex systems which combine the features of concurrent transformation of multiple variables in each elementary reaction event, and nonlinear relations between states and their rates of…

Chemical Physics · Physics 2017-12-06 Eric Smith , Supriya Krishnamurthy

Chemical systems are interpreted through the species they contain and the reactions they may undergo, i.e., their chemical reaction network (CRN). In spite of their central importance to chemistry, the structure of CRNs continues to be…

Statistical Mechanics · Physics 2025-06-17 Alex Blokhuis , Martijn van Kuppeveld , Daan van de Weem , Robert Pollice

We derive the nonequilibrium conductance matrix for open stationary Chemical Reaction Networks (CRNs) described by a deterministic mass action kinetic equation. As an illustration, we determine the nonequilibrium conductance matrix of a CRN…

Statistical Mechanics · Physics 2025-06-27 Paul Raux , Christophe Goupil , Gatien Verley

We consider how to generate chemical reaction networks (CRNs) from functional specifications. We propose a two-stage approach that combines synthesis by satisfiability modulo theories and Markov chain Monte Carlo based optimisation. First,…

Emerging Technologies · Computer Science 2015-08-19 Neil Dalchau , Niall Murphy , Rasmus Petersen , Boyan Yordanov

Chemical reaction networks (CRNs) model systems where molecules interact according to a finite set of reactions such as $A + B \to C$, representing that if a molecule of $A$ and $B$ collide, they disappear and a molecule of $C$ is produced.…

Computational Complexity · Computer Science 2026-01-21 David Doty , Ben Heckmann
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