Several Types Of Biological Models Of Almost Periodic Solutions

Almost periodic solution of biological models is an important part of study for the existence and stability of ecological models.Now,ecological model for almost periodic solutions has been undertaken in a number of research efforts,and achieved certain results,but these studies do less on almost periodic solution of biological models on time scales and almost periodic solution of a delayed single population model with feedback control and hereditary effect.Therefore,in this thesis,we will discuss the almost periodic solutions of hematopoiesis model with multiple time-varying delays on time scales?the almost periodic solutions of an impulsive Lasota-Wazewska model with multiple time-varying delays on time scales?a delayed single population model with feedback control and hereditary effect.This paper is organized as follows:Firstly,we discuss the almost periodic solutions of hematopoiesis model with multiple time-varying delays on time scales.Based on some basic results about almost periodic dynamic equations on time scales,and employing the contraction mapping principle and constructing some suitable discrete Lyapunov functionals,we obtain some sufficient conditions for the existence and global asymptotic stability of the almost periodic solution to the model.In addition,we present an example to show our results are feasible.Secondly,we discuss the almost periodic solutions of impulsive Lasota-Wazewsk-a model with multiple time-varying delays on time scales.Based on some basic results about almost periodic dynamic equations on time scales,and employing the contraction mapping principle and applying Gronwall-Bellman's inequality,we obtain some sufficient conditions for the existence and exponential stability of the almost periodic solution to the model.Moreover,we give an example to illustrate our main results.Finally,we consider a delayed single population model with feedback control and hereditary effect.Under proper conditions,we employ a novel proof to establish some criteria for ensuring that the permanence of the model.Furthermore,by applying the definition of an almost periodic function,we obtain sufficient conditions for the existence of positive almost periodic solutions for the model.Some new results are obtained.Our results supplement some known results.