一类具有阶段结构的时滞生态流行病模型周期解  

Periodic solutions of delayed eco-epidemiological model with stage structure

作　　者：张子振[1] 储煜桂 Zhang Zizhen;Chu Yugui(School of Management Science and Engineering,Anhui University of Financeand Economics,Bengbu 233030,China)

机构地区：[1]安徽财经大学管理科学与工程学院

出　　处：《南京理工大学学报》2018年第6期756-762,共7页Journal of Nanjing University of Science and Technology

基　　金：国家自然科学基金(61773181);安徽省高校优秀青年人才支持计划(gxyq ZD2018044)

摘　　要：为了控制疾病的传播,研究一类食饵种群具有阶段结构、捕食者种群具有疾病的时滞捕食系统模型。以捕食者种群疾病的潜伏期时滞为分岔参数,通过分析相应特征方程根的分布情况,讨论了模型正平衡点局部渐近稳定和存在Hopf分岔的充分条件。利用规范型理论和中心流形定理推导出确定Hopf分岔方向和分岔周期解稳定性的显式公式。利用仿真示例验证了结果的正确性。A delayed eco-epidemiological model with a stage structure for the prey and a transmissible disease spreading in the predator is investigated to control disease.The necessary conditions of the local stability of the positive equilibrium and the existence of a Hopf bifurcation are discussed by regarding the latent delay of the predator as the bifurcating parameter and analyzing the distribution of the roots of the associated characteristic equation.Explicit formulas determining the direction of the Hopf bifurcation and the stability of the bifurcation periodic solutions are derived by using the normal form theory and the center manifold theorem.The obtained results are verified by a numerical example.

关 键 词：阶段结构 时滞 生态流行病模型 食饵种群 捕食者种群 规范型理论 中心流形定理 

分 类 号：O175.12[理学—数学]