Several Types Of Biological Models Of Periodic And Almost Periodic Solutions

Periodic and almost periodic solution of biological models is an important part of study for the existence and stability of ecological models. Now, ecological model for periodic solution and almost periodic solutions has been undertaken in a number of research efforts, and achieved certain results, but these studies do not take into account the impulsive, feedback control, harvesting term and other ecological factors. Therefore, in this thesis, we will discuss a multiple delayed Hassell-Varley type functional response prey-predator system with nonlinear harvesting term、a discrete Hassell-Varley response function predator-prey system with feedback control、two types of hematopoiesis with impulsive terms. This paper is organized as follows:Firstly, we discuss the almost periodic solution of two hematopoiesis models. Basing on the works of Bainov and Samoilenko on the impulsive differential equation, and employing the contraction mapping principle and applying Gronwall-Bellman’s inequality, sufficient conditions are established to prove the existence and exponential stability of positive almost periodic solution for delaymodel of hematopoiesis with nonlinear impulsive. We found a small, low -pulse stability of impulsive term, the system of almost periodic solutions exist and are exponential stability.Secondly, we discuss a discrete Hassell-Varley response function predator-prey system with feedback control. First, sufficient conditions are established for the permanence of the system. Then, assuming that the coefficients of the system is almost periodic sequences, we obtain conditions for the existence and unique of the almost periodic solution by the theory on almost periodic solution of difference equation which were proposed by Cheban and Mammmana. Moreover, the almost periodic solution we obtained is uniformly asymptotically stable.Finally, we consider the effects of nonlinear harvesting term to Hassell-Varley type functional response prey-predator system. Currently, many scholars are discussed linear capture effects on populations of states. But, a multiple delayed Hassell-Varley type functional response prey-predator system with nonlinear harvesting term is investigated. In recent years, scholars study shows that harvesting term will have an important impact on the dynamic behavior of the system. By using Gaines andMawhin’s continuation theorem of coincidence degree theory, a set of sufficient conditions are obtained to guarantee the existence of positive periodic solutions of the system. At last, numerical simulation is given to illustrate the feasibility of our result. We get the mean value of the intrinsic rate of population is greater than the upper bound of capture, which requires us to avoid excessive capture to ensure the development cycle of the ecosystem. Therefore, our result has an important significance in ecological protection. In addition, the model and the result we got is the improvement and extension of some of the known model and conclusion, the purpose is to make it more rich biological significance.