Analysis of Quasi-Dynamic Ordinary Differential Equations and the Quasi-Dynamic Replicator

Christopher Griffin; Libo Jiang; Rongling Wu

Analysis of Quasi-Dynamic Ordinary Differential Equations and the Quasi-Dynamic Replicator

We study the mathematical properties of the quasi-dynamic ordinary differential equations defined empirically in [Chen et al. An omnidirectional visualization model of personalized gene regulatory networks, \textit{npj Systems Biology and Applications}, 5(1):38, 2019]. In particular, we show how the allometric scaling mentioned in that work emerges naturally from the generalized Lotka-Volterra model under the quasi-dynamic ordinary differential equations paradigm. We then define and study the proportional quasi-dynamic ordinary differential equations and discuss the relationship of this equation system to both the classical and discrete time replicator dynamics. We prove asymptotic properties of these systems for large and small populations and show that there exist populations for which the proportion of the population varies cyclically as a function of total logarithmic population size.

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Metadata

Work Title	Analysis of Quasi-Dynamic Ordinary Differential Equations and the Quasi-Dynamic Replicator
Access	Open Access
Creators	Christopher Griffin Libo Jiang Rongling Wu
Keyword	population dynamics evolutionary game cyclic games niche index
License	In Copyright (Rights Reserved)
Work Type	Article
Acknowledgments	NSF DMS-1814876
Publisher	Physica A
Publication Date	2020
Deposited	March 04, 2021

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Analysis of Quasi-Dynamic Ordinary Differential Equations and the Quasi-Dynamic Replicator

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View: QDODE-Short-ArXiv.pdf

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Work History

Version 1
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Analysis of Quasi-Dynamic Ordinary Differential Equations and the Quasi-Dynamic Replicator

Files

View: QDODE-Short-ArXiv.pdf

Metadata

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Work History

Version 1 published

Version 1
published