Permanence Of Several Stage-structured Predator-prey Systems

Biomathematics is a brink subject between biology and mathematics,which studies and solves biological problem by means of mathematical method,and proceed with theoretical study to mathematical method that relates to biology.The population dynamics is one important branches of it.Three models for population dynamics are studied in the thesis.The study for them are great theoretical and practical significance.The survival and development of biotic population is not depart from its living environment.In the resource limited environment,could the wild animals be coexistence for long-term under the animals' law of the jungle? To keep the biology's variety of the nature,the permanence of biotic population is a significant and comprehensive problem in biomathematics.First,a stage-structured three-species predator-prey system is proposed and analyzed.Based on the comparison theorem, some sufficient and necessary conditions are derived for permanence of the system. Later,two examples are presented to illustrate the application of our main results.Based on chapter 2,a delayed stage-structured three-species predator-prey model with Hollingâ…¡and Beddington-DeAngelis functional responses is investigated. A set of sufficient and necessary conditions which guarantee the predator and prey species to be permanent are obtained.In addition,sufficient conditions are derived for the existence of positive periodic solutions to the system.Numeric simulations show the feasibility of the main results.Finally,a stage-structured Beddington-DeAngelis functional responses predator-prey model with time delay and impulsive perturbations on predator is considered. Sufficient conditions of the global attractivity of prey-extinction periodic solution and the permanence of the system are obtained.We also prove that all solutions of the system are uniformly ultimately bounded.Our results provide reliable tactic basis for the practical pest management.