English
Related papers

Related papers: Chemical systems with limit cycles

200 papers

Chemically reacting flows are common in engineering, such as hypersonic flow, combustion, explosions, manufacturing processes and environmental assessments. For combustion, the number of reactions can be significant (over 100) and due to…

Machine Learning · Computer Science 2021-04-06 Thomas S. Brown , Harbir Antil , Rainald Löhner , Fumiya Togashi , Deepanshu Verma

Chemical Reaction Networks (CRNs) are a well-established model of distributed computing characterized by quantities of molecular species that can transform or change through applications of reactions. A fundamental problem in CRNs is the…

Computational Complexity · Computer Science 2026-04-21 Divya Bajaj , Bin Fu , Ryan Knobel , Austin Luchsinger , Aiden Massie , Pablo Santos , Ramiro Santos , Robert Schweller , Evan Tomai , Tim Wylie

Power law dynamics is used to describe the stability behavior in metabolic networks such as chemical reaction networks (CRN's). These systems allow multiple steady states within a single stoichiometric class. On the other side thermodynamic…

Dynamical Systems · Mathematics 2020-07-10 Gunther Friedrich Neumann

Reaction networks are a general formalism for describing collections of classical entities interacting in a random way. While reaction networks are mainly studied by chemists, they are equivalent to Petri nets, which are used for similar…

Mathematical Physics · Physics 2021-11-23 John C. Baez

We describe a large class of chemical reaction networks, those endowed with a subtle structural property called concordance. We show that the class of concordant networks coincides precisely with the class of networks which, when taken with…

Molecular Networks · Quantitative Biology 2011-09-15 Guy Shinar , Martin Feinberg

We present two quantitative behavioral equivalences over species of a chemical reaction network (CRN) with semantics based on ordinary differential equations. Forward CRN bisimulation identifies a partition where each equivalence class…

Logic in Computer Science · Computer Science 2015-07-16 Luca Cardelli , Mirco Tribastone , Max Tschaikowski , Andrea Vandin

The stochastic kinetics of BRN are described by a chemical master equation (CME) and the underlying laws of mass action. The CME must be usually solved numerically by generating enough traces of random reaction events. The resulting…

Molecular Networks · Quantitative Biology 2023-06-21 Pavel Loskot

In this paper, it is presented a methodology for implementing arbitrarily constructed time-homogenous Markov chains with biochemical systems. Not only discrete but also continuous-time Markov chains are allowed to be computed. By employing…

Molecular Networks · Quantitative Biology 2018-02-16 Chuan Zhang , Ziyuan Shen , Wei Wei , Jing Zhao , Zaichen Zhang , Xiaohu You

Reaction networks have been widely used as generic models in diverse areas of applied sciences, such as biology, chemistry, ecology, epidemiology, and computer science. A reaction network incorporating noisy effects is modeled as a…

Molecular Networks · Quantitative Biology 2026-05-12 Chuang Xu

Chemical reaction networks (CRNs) are a standard formalism used in chemistry and biology to reason about the dynamics of molecular interaction networks. In their interpretation by ordinary differential equations, CRNs provide a…

Quantitative Methods · Quantitative Biology 2020-07-28 Mathieu Hemery , François Fages , Sylvain Soliman

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…

Statistical Mechanics · Physics 2009-02-20 Akinori Awazu , Kunihiko Kaneko

We show that some natural output conventions for error-free computation in chemical reaction networks (CRN) lead to a common level of computational expressivity. Our main results are that the standard consensus-based output convention have…

Emerging Technologies · Computer Science 2017-07-11 Robert Brijder , David Doty , David Soloveichik

Chemical reaction networks, or CRNs, are known to stably compute semilinear Boolean-valued predicates and functions, provided that all reactions are irreversible. However, this property does not hold for wet-lab implementations, as all…

Computational Complexity · Computer Science 2026-04-17 Ravi Kini , David Doty

Many reaction networks arising in applications are multistationary, that is, they have the capacity for more than one steady state; while some networks exhibit absolute concentration robustness (ACR), which means that some species…

Dynamical Systems · Mathematics 2024-11-20 Nidhi Kaihnsa , Tung Nguyen , Anne Shiu

Most differential equations found in chemical reaction networks (CRNs) have the form $dx/dt=f(x)= Sv(x)$, where $x$ lies in the nonnegative orthant, where $S$ is a real matrix (the stoichiometric matrix) and $v$ is a column vector…

Dynamical Systems · Mathematics 2011-04-19 J. William Helton , Igor Klep , Vitaly Katsnelson

Chemical reaction network theory provides powerful tools for rigorously understanding chemical reactions and the dynamical systems and differential equations that represent them. A frequent issue with mathematical analyses of these networks…

Quantitative Methods · Quantitative Biology 2025-12-23 Joseph M. Sauder , Bruce P. Ayati , Ryan Kinser

Models of biochemical networks are frequently high-dimensional and complex. Reduction methods that preserve important dynamical properties are therefore essential in their study. Interactions between the nodes in such networks are…

Molecular Networks · Quantitative Biology 2013-08-23 Alan Veliz-Cuba , Ajit Kumar , Kresimir Josic

To unveil the logic of cell from a level of chemical reaction dynamics, we need to clarify how ensemble of chemicals can autonomously produce the set of chemical, without assuming a specific external control echanism. A cell consists of a…

Molecular Networks · Quantitative Biology 2007-05-23 Kunihiko Kaneko

We investigate a broad family of non weakly reversible stochastically modeled reaction networks (CRN), by looking at their steady-state distributions. Most known results on stationary distributions assume weak reversibility and zero…

Probability · Mathematics 2023-02-20 Linard Hoessly , Christian Mazza

To what extent do the characteristic features of a chemical reaction network reflect its purpose and function? In general, one argues that correlations between specific features and specific functions are key to understanding a complex…

Statistical Mechanics · Physics 2012-03-22 Sang Hoon Lee , Sebastian Bernhardsson , Petter Holme , Beom Jun Kim , Petter Minnhagen