S-invariant Termwise Addition of Reactions Via Reaction Vector Multiples (STAR-RVM) Transformation

IF 1 Q1 MATHEMATICS
Daryl Magpantay
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引用次数: 0

Abstract

Interest in connecting Chemical Reactions Network Theory (CRNT) and evolutionary game theory (EGT) arise viewing the tools of network in the analysis of evolutionary games. Here, the evolution of population species is studied as a biological phenomenon and describing the rate of such changes through a replicator system becomes a focus. A set of polynomial kinetics (POK) may then be introduced for the realization of this replicator system and this is based on the polynomial payoff functions defined in the game. These polynomial kinetics result in polynomial dynamical systems of ordinary differential equations, which are used in analyzing strategies that prove beneficial under certain conditions. From the CRNT point of view, it now becomes interesting to study a superset of POK, which we call poly-PL kinetics (PYK). This set is formed by getting nonnegative linear combinations of power law functions. Thus, PYK contains the set PLK of power law kinetics as mono-PL kinetics with coefficient 1. Seeing this connection between CRNT and EGT and what are known about power law kinetics, we take an interest in studying PYK systems. This paper aims to analyze different ways of transforming PYK to PLK in order to explore some approaches for CRNT analysis of PYK systems. Specifically, we study a network structure-oriented transformations using the S-invariant term-wise addition of reactions (STAR) Via Reaction Vector Multiples (RVM) that transform PYK to PLK systems.
通过反应向量倍数(STAR-RVM)变换的s不变逐项加法
将化学反应网络理论(CRNT)与进化博弈论(EGT)联系起来的兴趣出现在分析进化博弈的网络工具中。在这里,种群物种的进化是作为一种生物现象来研究的,通过复制子系统来描述这种变化的速度成为一个焦点。一组多项式动力学(POK)可以用来实现这个复制系统,这是基于游戏中定义的多项式收益函数。这些多项式动力学得到常微分方程的多项式动力系统,用于分析在某些条件下证明是有益的策略。从CRNT的角度来看,现在研究POK的超集变得很有趣,我们称之为聚pl动力学(PYK)。这个集合是由幂律函数的非负线性组合形成的。因此,PYK包含幂律动力学的集合PLK为系数为1的单pl动力学。看到CRNT和EGT之间的这种联系以及幂律动力学的已知内容,我们对PYK系统的研究产生了兴趣。本文旨在分析PYK转换为PLK的不同方法,以探索PYK系统的CRNT分析方法。具体来说,我们研究了一个面向网络结构的转换,该转换使用s不变逐项加法反应(STAR),通过反应向量倍数(RVM)将PYK转换为PLK系统。
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来源期刊
CiteScore
1.30
自引率
28.60%
发文量
156
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