中北大学学报（自然科学版）2025，Vol.46Issue(1)：64-75,12.DOI:10.62756/jnuc.issn.1673-3193.2024.02.0009
具有密度依赖演化博弈模型的随机稳定性分析
Analysis of Stochastic Stability on Evolutionary Games Model with Density Dependence
摘要
Abstract
Evolutionary games provide a new perspective to examine and understand interactive behaviors in complex systems,and provide powerful tools and methods for research in several fields.Much of the existing literature focuses on the study of the dynamical behavior of deterministic ecological game models,and doesn't explore the influence of population and environmental stochasticity on the dynamics of ecologi-cal evolutionary games.Thus,this paper considered environmental random noise,and constructed a sto-chastic evolutionary game dynamics model with density dependence considering individual birth and death rates.Dynamics of the constructed model was analyzed to confirm the effect of random noise on the trends of ecological evolution.Firstly,the effect of noise on ecological evolutionary game models with density dependence is shown by analyzing the equilibrium points and their stability of the dynamical mod-els of ecological evolutionary games with density dependence indeed,and by proving the stability of the corresponding stochastic evolutionary game models using stochastic Lyapunov theory.Secondly,the threshold value of environmental noise was obtained from the study.When the environmental noise value is greater than the threshold,population extinction and phenotype disappearance are almost surely exponen-tially stable.Conversely,when the environmental noise value is less than a certain threshold,the fre-quency of phenotypes with higher birth rates is persistent in mean.Finally,the theoretical verification and numerical simulation were carried out with the deer hunting game model as an example to confirm the validity and feasibility of the theory.This result also provides a new idea for understanding how environ-mental fluctuations contribute to the evolution of phenotypic diversity.关键词
演化博弈/密度依赖/几乎必然指数稳定/随机Lyapunov理论/稳定性Key words
evolutionary game/density dependence/almost sure exponential stability/stochastic Lyapu-nov theory/stability分类
数学引用本文复制引用
孙霞,呼文军,刘婕..具有密度依赖演化博弈模型的随机稳定性分析[J].中北大学学报（自然科学版）,2025,46(1):64-75,12.基金项目
国家自然基金资助项目(12371494) （12371494）
山西省自然科学基金资助项目(2021L561) （2021L561）
