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.

Files

Metadata

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

Versions

Analytics

Collections

This resource is currently not in any collection.

Work History

Version 1
published

  • Created
  • Added Creator Christopher Griffin
  • Added Creator Libo Jiang
  • Added Creator Rongling Wu
  • Updated Acknowledgments Show Changes
    Acknowledgments
    • NSF DMS-1814876
  • Added QDODE-Short-ArXiv.pdf
  • Updated License Show Changes
    License
    • https://rightsstatements.org/page/InC/1.0/
  • Published
  • Updated
  • Updated