化学反应系统的稳定性、离散化和分岔分析

IF 2.9 2区化学 Q2 CHEMISTRY, MULTIDISCIPLINARY

Match-Communications in Mathematical and in Computer Chemistry Pub Date : 2023-01-01 DOI:10.46793/match.90-1.151d

Qamar Din, Umer Saeed

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引用次数: 1

摘要

化学反应揭示了所有类型的奇异行为，即多稳定性、振荡性、混沌性或多平稳性。速率方程的数学框架使我们能够讨论化学反应的稳态、稳定性和振荡行为。研究了由动力学微分方程导出的两种化学反应的非线性微分方程控制的平面三次动力系统。研究了系统具有唯一的正稳态。此外，围绕系统的正稳态研究了系统的局部动力学。给出了正平衡Hopf分岔的存在性和方向。为了修正分岔行为，研究了分岔控制。针对连续化学反应系统，提出了一种保持相合的离散化方法，并对其定性行为进行了研究。通过数值模拟和分岔图来说明数学研究。

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Stability, Discretization, and Bifurcation Analysis for a Chemical Reaction System

Chemical reactions reveal all types of exotic behavior, that is, multistability, oscillation, chaos, or multistationarity. The mathematical framework of rate equations enables us to discuss steadystates, stability and oscillatory behavior of a chemical reaction. A planar cubic dynamical system governed by nonlinear differential equations induced by kinetic differential equations for a two-species chemical reaction is studied. It is investigated that system has unique positive steady state. Moreover, local dynamics of system is studied around its positive steady state. Existence and direction of Hopf bifurcation about positive equilibrium are carried out. In order to modify the bifurcating behavior, bifurcation control is investigated. Keeping in mind, a consistency preserving discretization for continuous chemical reaction system, a discrete counterpart is proposed, and its qualitative behavior is investigated. Numerical simulation along with bifurcation diagrams are provided to illustrate the mathematical investigations.

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来源期刊

Match-Communications in Mathematical and in Computer Chemistry 化学-化学综合

CiteScore

4.40

自引率

26.90%

发文量

审稿时长

2 months

期刊介绍： MATCH Communications in Mathematical and in Computer Chemistry publishes papers of original research as well as reviews on chemically important mathematical results and non-routine applications of mathematical techniques to chemical problems. A paper acceptable for publication must contain non-trivial mathematics or communicate non-routine computer-based procedures AND have a clear connection to chemistry. Papers are published without any processing or publication charge.