KMS Of Academy of mathematics and systems sciences, CAS
| Hybrid matrix models and their population dynamic consequences | |
| Tang, S | |
| 2003-05-01 | |
| Source Publication | ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
 |
| ISSN | 0764-583X |
| Volume | 37Issue:3Pages:433-450 |
| Abstract | 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. |
| Keyword | hybrid matrix model birth pulse supercritical flip bifurcation stroboscopic map generation delay |
| DOI | 10.1051/m2an:2003036 |
| Language | 英语 |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000184347900002 |
| Publisher | E D P SCIENCES |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/18500 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Tang, S |
| Affiliation | Acad 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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