具有生育脉冲的单种群阶段结构离散模型复杂性分析  

Analyses of complexities in a single-species discrete model with stage structure and birth pulses

作　　者：高淑京[1] 陈兰荪[1] 

机构地区：[1]大连理工大学应用数学系

出　　处：《大连理工大学学报》2006年第4期611-614,共4页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(10171106);广东省自然科学基金资助项目(020586)

摘　　要：研究了两个单种群阶段结构离散模型.对没有脉冲效应的模型,得到了平凡平衡态和正平衡态全局渐近稳定的充分条件.对具有密度依赖生育脉冲的模型,运用频闪映射,结合分支理论和数值分析,得到了正平衡态的存在性、稳定性;以出生率作为分支参数的分支图呈现出包括混沌带、周期倍增、周期对分、多个吸引子共存等复杂的动力学行为.这说明生育脉冲能使系统出现各种周期震荡,使系统的动力学行为变得非常复杂.Two sigle-species discrete models with stage structure are proposed and analyzed. For the model without impulse, sufficient conditions for global asymptotic stability of trivial equilibrium and positive equilibrium are obtained. For the model with time-dependent birth pulses, using the stroboscopic map, the theory on bifurcation and numerical analysis, the existence and stability of the positive equilibrium are obtained. Bifurcation diagrams are constructed with the birth rate as the bifurcation parameter, and they are observed to display complex dynamic behaviors, including chaotic bands, doubling-bifurcation, halving-bifurcation and coexistence of several attractors. It is pointed out that birth pulses provide a natural period or cyclicity that makes the dynamic behaviors more complicated.

关 键 词：生育脉冲 阶段结构 离散模型 混沌 

分 类 号：O175.1[理学—数学]