具非线性收获项和S-型时滞Lasota-Wazewska模型的概周期解  

Almost Periodic Solution to Lasota-Wazewska Model with a Nonlinear Harvesting Term and S-type Delay

作　　者：周辉[1,2] 王文[2] 周宗福[3] 

机构地区：[1]中国科学技术大学数学科学学院,合肥230039 [2]合肥师范学院数学与统计学院,合肥230601 [3]安徽大学数学科学学院,合肥230039

出　　处：《应用数学学报》2017年第3期471-480,共10页Acta Mathematicae Applicatae Sinica

基　　金：安徽自然科学基金(1608085MA12;1708085MA16);安徽省高校优秀青年人才项目(gxyq2017048);安徽省高校省级自然科学重点项目(KJ2017A937)资助

摘　　要：本文应用锥上的不定点理论,研究了带有非线性收获项和S-型时滞概周期LasotaWazewska模型正解的存在唯一性。得到了该模型的正概周期解存在唯一的充分条件,在该条件假设下,利用一般的压缩影像原理不能得到所研究模型解的存在性.进而,本文又给出了此解的指数收敛的要求.本文最后给出了一个实例说明了对顺型假设和结果的可行性.By utilizing a fixed theorem in cones, we study the existence of the unique positive almost periodic solution for a generalized Lasota-Wazewska model with a nolinear harvesting terms. Some sufficient conditions which ensure the existence of a unique positive almost periodic solution are derived and it cannot be obtained by the contraction mapping principle. Furthermore, under proper conditions, we establish some criteria to ensure that all solutions of this model converge exponentially to a positive almost periodic solution. An example is provided to illustrate the effectiveness of the proposed result.

关 键 词：概周期解 非线性收获 指数收敛 

分 类 号：O175.13[理学—数学] O193[理学—基础数学]