Study Of Two Non-autonomous Impulsive Stochastic Delay Single Species Models With Predation Term

In the real world the survival and development of the population will be affected by many factors,such as environmental noise,time delay,impulsive and predation.Therefore,it is necessary to consider these factors in the establishment of ecological models.In this thesis,some theories related to stochastic differential equations,functional analysis and impulsive differential equations are used to investigate the permanence and extinction of two non-autonomous impulsive stochastic delay single-species models.Moreover,several specific numerical examples are given.The whole thesis has been divided into four chapters:The first chapter outlines the research backgrounds,research significances and research status as well as the main works that we have done in this thesis.In the second chapter,some notations related to this paper are given,and some definitions,lemmas and inequalities are introduced.In the third chapter,two types of non-autonomous impulsive stochastic delay single-species models with predation term are established and discussed.Sufficient conditions for stochastic permanence of two systems are derived.Finally,some specific numerical examples are provided to illustrate the effectiveness of our theoretical results.In the forth chapter,two types of non-autonomous impulsive stochastic delay single-species models with predation term are proposed and investigated by taking Lévy noise into account.A good understanding of extinction,non-persistence in the mean,weak persistence and stochastic permanence is obtained.Finally,numerical simulations carried out for resulting systems confirm our theoretical analysis results.