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379 results on '"Dochain, Denis"'

38. Capturing persistence of delayed complex balanced chemical reaction systems via decomposition of semilocking sets

Author

Zhang, Xiaoyu, Gao, Chuanhou, and Dochain, Denis

Subjects
FOS: Mathematics, Dynamical Systems (math.DS), Mathematics - Dynamical Systems
Abstract

With the increasing complexity of time-delayed systems, the diversification of boundary types of chemical reaction systems poses a challenge for persistence analysis. This paper focuses on delayed complex balanced mass action systems (DeCBMAS) and derives that some boundaries of a DeCBMAS can not contain an $\omega$-limit point of some trajectory with positive initial point by using the method of semilocking set decomposition and the property of the facet, further expanding the range of persistence of delayed complex balanced systems. These findings demonstrate the effectiveness of semilocking set decomposition to address the complex boundaries and offer insights into the persistence analysis of delayed chemical reaction network systems.

Published
2023

39. Chemical relaxation oscillator designed to control molecular computation

Author

Shi, Xiaopeng, Gao, Chuanhou, and Dochain, Denis

Subjects
FOS: Mathematics, Dynamical Systems (math.DS), Mathematics - Dynamical Systems
Abstract

Embedding efficient calculation instructions into biochemical system has always been a research focus in synthetic biology. One of the key problems is how to sequence the chemical reaction modules that act as units of computation and make them alternate spontaneously. Our work takes the design of chemical clock signals as a solution and presents a $4$-dimensional chemical oscillator model based on relaxation oscillation to generate a pair of symmetric clock signals for two-module regulation. We give detailed dynamical analysis of the model and discuss how to control the period and occurrence order of clock signals. We also demonstrate the loop control of molecular computations and provide termination strategy for them. We can expect that our design for module regulation and loop termination will help advance the embedding of more complicate calculations into biochemical environments.

Published
2023

46. On the relation between omega-limit set and boundaries of mass-action chemical reaction networks

Author

Xiaoyu Zhang, Zhou Fang, Chuanhou Gao, Dochain, Denis, and UCL - SST/ICTM/INMA - Pôle en ingénierie mathématique

Subjects
chemical reaction network, ω-limit set, Lyapunov Function PDEs, mass-action system, boundaries
Abstract

ω-limit set can be used to understand the long term behavior of a dynamical system. In this paper, we use the Lyapunov function PDEs method, developed in our previous work, to study the relation between ω-limit points and boundaries for chemical reaction networks equipped with mass-action kinetics. Using the solution of the PDEs, some new checkable criteria are proposed to diagnose non ω-limit points of the network system. These criteria are successfully applied to verify that non-semilocking boundary points and some semilocking boundary points are not ω-limit points. Further, we derive the ω-limit theorem that precludes the limit cycle of some biochemical network systems. The validity of the results are demonstrated through some abstract and practical examples of chemical reaction networks.

Published
2023

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