English
Related papers

Related papers: Chemical systems with limit cycles

200 papers

Reaction networks have become a major modelling framework in the biological sciences from epidemiology and population biology to genetics and cellular biology. In recent years, much progress has been made on stochastic reaction networks…

Probability · Mathematics 2025-08-14 Linard Hoessly , Carsten Wiuf , Panqiu Xia

Principles of feedback control have been shown to naturally arise in biological systems and successfully applied to build synthetic circuits. In this work we consider Biochemical Reaction Networks (CRNs) as a paradigm for modelling…

Systems and Control · Computer Science 2019-03-26 Max Whitby , Luca Cardelli , Marta Kwiatkowska , Luca Laurenti , Mirco Tribastone , Max Tschaikowski

Step Chemical Reaction Networks (step CRNs) are an augmentation of the Chemical Reaction Network (CRN) model where additional species may be introduced to the system in a sequence of ``steps.'' We study step CRN systems using a weak subset…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-05-03 Rachel Anderson , Bin Fu , Aiden Massie , Gourab Mukhopadhyay , Adrian Salinas , Robert Schweller , Evan Tomai , Tim Wylie

Chemical reaction networks (CRNs) model the behavior of molecules in a well-mixed system. The emerging field of molecular programming uses CRNs not only as a descriptive tool, but as a programming language for chemical computation.…

Computational Complexity · Computer Science 2015-09-04 Adam Case , Jack H. Lutz , D. M. Stull

Much of the theory on chemical-reaction networks (CRNs) has been developed in the ideal-solution limit, where interactions between the solutes are negligible. However, there is a large variety of phenomena in biological cells and…

Biological Physics · Physics 2022-12-09 Ander Movilla Miangolarra , Michele Castellana

The chemical reaction network (CRN) is a widely used formalism to describe macroscopic behavior of chemical systems. Available tools for CRN modelling and simulation require local access, installation, and often involve local file storage,…

Computational Engineering, Finance, and Science · Computer Science 2015-12-07 Peter Banda , Drew Blount , Christof Teuscher

Chemical Reaction Neural Networks (CRNNs) have emerged as an interpretable machine learning framework for discovering reaction kinetics directly from data, while strictly adhering to the Arrhenius and mass action laws. However, standard…

Chemical Physics · Physics 2026-05-15 Benjamin C. Koenig , Sili Deng

The use of mathematical models has helped to shed light on countless phenomena in chemistry and biology. Often, though, one finds that systems of interest in these fields are dauntingly complex. In this paper, we attempt to synthesize and…

Molecular Networks · Quantitative Biology 2007-09-04 Mark Lipson

Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to…

Probability · Mathematics 2023-04-12 Felipe A. Campos , Simone Bruno , Yi Fu , Domitilla Del Vecchio , Ruth J. Williams

Many important phenomena in biochemistry and biology exploit dynamical features such as multi-stability, oscillations, and chaos. Construction of novel chemical systems with such rich dynamics is a challenging problem central to the fields…

Molecular Networks · Quantitative Biology 2026-05-04 Alexander Dack , Benjamin Qureshi , Thomas E. Ouldridge , Tomislav Plesa

Under suitable assumptions, the dynamic behaviour of a chemical reaction network is governed by an autonomous set of polynomial ordinary differential equations over continuous variables representing the concentrations of the reactant…

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

The asymptotic properties of some Markov processes associated to stochastic chemical reaction networks (CRNs) driven by the kinetics of the law of mass action are analyzed. The scaling regime introduced in the paper assumes that the norm of…

Probability · Mathematics 2025-12-18 Lucie Laurence , Philippe Robert

We study the composability of discrete chemical reaction networks (CRNs) that stably compute (i.e., with probability 0 of error) integer-valued functions $f:\mathbb{N}^d\to\mathbb{N}$. We consider output-oblivious CRNs in which the output…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-06-04 Eric E. Severson , David Haley , David Doty

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

A family of results, referred to as inheritance results, tell us which enlargements of a chemical reaction network (CRN) preserve its capacity for nontrivial behaviours such as multistationarity and oscillation. In this paper, the following…

Dynamical Systems · Mathematics 2023-02-23 Murad Banaji

In this paper we introduce a formalism that allows to describe the response of a part of a biochemical system in terms of renewal equations. In particular, we examine under which conditions the interactions between the different parts of a…

Analysis of PDEs · Mathematics 2023-09-06 E. Franco , B. Kepka , J. J. L. Velázquez

The Turing completeness of continuous chemical reaction networks (CRNs) states that any computable real function can be computed by a continuous CRN on a finite set of molecular species, possibly restricted to elementary reactions, i.e.…

Molecular Networks · Quantitative Biology 2022-06-22 Mathieu Hemery , François Fages

We continue recent attempts to put together concepts and results of Chemical Reaction Networks theory (CRNT) and Mathematical Epidemiology (ME), for solving problems of stability of positive ODEs. We provide first an elegant CRN-flavored…

Molecular Networks · Quantitative Biology 2026-04-21 Florin Avram , Rim Adenane , Andrei-Dan Halanay

A decomposition of a chemical reaction network (CRN) is produced by partitioning its set of reactions. The partition induces networks, called subnetworks, that are "smaller" than the given CRN which, at this point, can be called parent…

Molecular Networks · Quantitative Biology 2021-09-15 Lauro L. Fontanil , Eduardo R. Mendoza

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…

Molecular Networks · Quantitative Biology 2012-04-26 Guy Shinar , Martin Feinberg