具有密度依赖的生育脉冲单种群阶段结构模型  

STAGE-STRUCTURED MODEL OF A SINGLE-SPECIES WITH DENSITY-DEPENDENT BIRTH PULSES

作　　者：张树文[1] 陈兰荪[2] 

机构地区：[1]集美大学理学院,厦门361021 [2]中国科学院数学与系统科学研究院数学研究所,北京100080

出　　处：《系统科学与数学》2006年第6期752-760,共9页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(10171106)和(40372111)资助课题.

摘　　要：给出具有密度依赖生育脉冲单种群阶段结构数学模型．通过研究其频闪映射所确定的离散动力系统,获得了具有生育脉冲的系统存在周期解及其稳定的阈值,当系统的参数超过阈值,存在一系列的分支并最终走向混沌,这说明生育脉冲使系统动力学行为变得非常复杂,提供了一个自然的周期,而使系统从倍周期分支到混沌．A stage-structured mathematical model of a single-species with density-dependent birth pulses is proposed. We abtain exact periodic solutions of the system with birth pulses and threshold for stablity of peridic solutions by studying the discrete dynamical system determinded by the stroboscopic map. When the parameter of the system exceeds the threshold, there is a characteristic sequence of bifurcations, leading to chaos. This illustrates that birth pulses reslut in the complexity of dynamical behavior of the system, provide a natural period, and allow for a period-doubling route leading to chaos.

关 键 词：密度依赖 生育脉冲 阈值 分支 周期解 混沌 

分 类 号：O175[理学—数学] Q141[理学—基础数学]