TY - JOUR
T1 - Analysis of quasi-dynamic ordinary differential equations and the quasi-dynamic replicator
AU - Griffin, Christopher
AU - Jiang, Libo
AU - Wu, Rongling
N1 - Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2020/10/1
Y1 - 2020/10/1
N2 - We study the mathematical properties of the quasi-dynamic ordinary differential equations defined empirically in Chen et al. (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.
AB - We study the mathematical properties of the quasi-dynamic ordinary differential equations defined empirically in Chen et al. (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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U2 - 10.1016/j.physa.2020.124422
DO - 10.1016/j.physa.2020.124422
M3 - Article
AN - SCOPUS:85081258370
SN - 0378-4371
VL - 555
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
M1 - 124422
ER -