# 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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size: 733 KB | mime_type: application/pdf | date: 2021-03-04

Work Title Analysis of Quasi-Dynamic Ordinary Differential Equations and the Quasi-Dynamic Replicator Open Access Christopher GriffinLibo JiangRongling Wu population dynamicsevolutionary game cyclic gamesniche index Article NSF DMS-1814876 Physica A 2020 March 04, 2021

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