Hybrid matrix models and their population dynamic consequences

doi:10.1051/m2an:2003036

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	Hybrid matrix models and their population dynamic consequences
	Tang, S
	2003-05-01
发表期刊	ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
ISSN	0764-583X
卷号	37 期号:3 页码:433-450
摘要	In this paper, the main purpose is to reveal what kind of qualitative dynamical changes a continuous age-structured model may undergo as continuous reproduction is replaced with an annual birth pulse. Using the discrete dynamical system determined by the stroboscopic map we obtain an exact periodic solution of system with density-dependent fertility and obtain the threshold conditions for its stability. We also present formal proofs of the supercritical flip bifurcation at the bifurcation as well as extensive analysis of dynamics in unstable parameter regions. Above this threshold, there is a characteristic sequence of bifurcations, leading to chaotic dynamics, which implies that the dynamical behavior of the single species model with birth pulses are very complex, including small-amplitude annual oscillations, large-amplitude multi-annual cycles, and chaos. This suggests that birth pulse, in effect, provides a natural period or cyclicity that allows for a period-doubling route to chaos. Finally, we discuss the effects of generation delay on stability of positive equilibrium (or positive periodic solution) and show that generation delay is found to act both as a destabilizing and a stabilizing effect.
关键词	hybrid matrix model birth pulse supercritical flip bifurcation stroboscopic map generation delay
DOI	10.1051/m2an:2003036
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000184347900002
出版者	E D P SCIENCES
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/18500
专题	中国科学院数学与系统科学研究院
通讯作者	Tang, S
作者单位	Acad Sinica, Acad Math & Syst Sci, Inst Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Tang, S. Hybrid matrix models and their population dynamic consequences[J]. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE,2003,37(3):433-450.
APA	Tang, S.(2003).Hybrid matrix models and their population dynamic consequences.ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE,37(3),433-450.
MLA	Tang, S."Hybrid matrix models and their population dynamic consequences".ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE 37.3(2003):433-450.