本文選題：狀態(tài)依賴(lài) + 周期解��； 參考：《蘭州理工大學(xué)》2017年碩士論文

【摘要】：作為數(shù)學(xué)和生物學(xué)相結(jié)合的新興交叉學(xué)科,生物數(shù)學(xué)模型的研究近百年來(lái)得到了長(zhǎng)足的發(fā)展.由于脈沖可以準(zhǔn)確地描述某種數(shù)量在某些定時(shí)刻的快速變化或跳躍的特性,脈沖微分方程普遍用于生物種群生長(zhǎng)發(fā)展的控制建模分析中.本文主要研究具有二次狀態(tài)依賴(lài)脈沖控制的捕食-食餌模型,分析在不同狀態(tài)依賴(lài)脈沖控制下的害蟲(chóng)治理模型的動(dòng)力學(xué)行為.首先研究了一種基于Leslie-Gower修改的具有Holling-II型功能反應(yīng)函數(shù)的狀態(tài)依賴(lài)脈沖控制的捕食-食餌模型,分別研究了不加脈沖控制的情況下的解的存在性以及具有狀態(tài)依賴(lài)脈沖控制下動(dòng)力學(xué)行為.其次研究了一種帶有二次狀態(tài)依賴(lài)脈沖控制的Holling-Ⅲ型的捕食者食餌模型,利用后繼函數(shù)、幾何分析方法、脈沖微分方程的Poincare-Bendixson環(huán)域定理分析了系統(tǒng)周期解的存在性,進(jìn)一步利用脈沖微分方程周期解的穩(wěn)定性理論和類(lèi)龐加萊準(zhǔn)則給出了系統(tǒng)周期解穩(wěn)定的充分條件.
[Abstract]:As a new interdisciplinary subject which combines mathematics and biology, the research of biological mathematical model has been greatly developed in the past hundred years. Because impulses can accurately describe the characteristics of a certain number of rapid changes or jumps at certain fixed times, impulsive differential equations are widely used in the control modeling and analysis of the growth and development of biological populations. In this paper, the predator-prey model with quadratic state dependent impulse control is studied, and the dynamic behavior of pest control model with different state dependent impulse control is analyzed. Firstly, a prey-prey model with state dependent impulse control with Holling-II type functional response function modified by Leslie-Gower is studied. The existence of solutions without impulsive control and the dynamic behavior under state-dependent impulsive control are studied respectively. Secondly, a predator-prey model of Holling- 鈪，

本文編號(hào)：1857759