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Hybrid matrix models and their population dynamic consequences
Tang, S
2003-05-01
Source PublicationESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
ISSN0764-583X
Volume37Issue:3Pages:433-450
AbstractIn 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.
Keywordhybrid matrix model birth pulse supercritical flip bifurcation stroboscopic map generation delay
DOI10.1051/m2an:2003036
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000184347900002
PublisherE D P SCIENCES
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/18500
Collection中国科学院数学与系统科学研究院
AffiliationAcad Sinica, Acad Math & Syst Sci, Inst Math, Beijing 100080, Peoples R China
Recommended Citation
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.
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