Dynamic Behavior Of Two Classes Of Competition And Mutualism Models With Imprecise Parameters

It is well known that population ecosystems are inevitably affected by internal and external factors which make the parameters of population ecosystems appear uncertainty.Fuzziness and randomness are two typical forms of uncertainty.The former mainly reflects the inaccuracy of parameters and the latter mainly reflects in certain random distribution of parameters.In this paper,the first model is a competition model with interval-valued parameters,which considers the effects of time delays and economic harvest.The second model is a stochastic mutualism model,which considers the impacts of coupling noise sources and impulsive perturbations.We analyze the dynamic behaviors of two types of models by applying the knowledge of ordinary differential equations,delay differential equations,impulsive differential equations and stochastic differential equations.Specific numerical examples are given to verify the feasibility of the theoretical findings.This thesis has been divided into four chapters as follows:The first chapter outlines the research backgrounds,research significances and research status as well as the main works that we have done in this paper.The second chapter gives some symbol descriptions related to this article and introduces some related definitions,lemmas and important inequalities.In the third chapter,a delayed competition model with saturation effect and interval-valued parameters is studied.Sufficient criteria for the existence,local and global asymptotic stability of the unique positive equilibrium are obtained.Also the existence of the eco-economic equilibrium point and optimal harvesting policy of the model in the absence of delay are discussed.In the fourth chapter,an impulsive stochastic mutualism model with saturation effect is studied.The dynamic properties of existence and uniqueness of global positive solution,stochastic permanence,extinction,permanence in time average and asymptotic pathwise estimation of this model are obtained.