Dynamics in a discrete-time predator-prey system with Allee effect
文献类型：期刊论文
| 作者 | Chen Xianwei2; Fu Xiangling3; Jing Zhujun2 |
| 刊名 | ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
 |
| 出版日期 | 2013 |
| 卷号 | 29期号:1页码:143-164 |
| ISSN号 | 0168-9673 |
| 关键词 | POPULATION-DYNAMICS CHAOS MODEL Predator-prey System Allee effect flip bifurcation Hopf bifurcation Marotto's chaos transient chaos invariant circle periodic window |
| 其他题名 | Dynamics in a Discrete-time Predator-prey System with Allee Effect |
| 英文摘要 | In this paper, dynamics of the discrete-time predator-prey system with Allee effect are investigated in detail. Conditions of the existence for flip bifurcation and Hopf bifurcation are derived by using the center manifold theorem and bifurcation theory, and then further illustrated by numerical simulations. Chaos in the sense of Marotto is proved by both analytical and numerical methods. Numerical simulations included bifurcation diagrams, Lyapunov exponents, phase portraits, fractal dimensions display new and rich dynamical behavior. More specifically, apart from stable dynamics, this paper presents the finding of chaos in the sense of Marotto together with a host of interesting phenomena connected to it. The analytic results and numerical simulations demostrates that the Allee constant plays a very important role for dynamical behavior. The dynamical behavior can move from complex instable states to stable states as the Allee constant increases (within a limited value). Combining the existing results in the current literature with the new results reported in this paper, a more complete understanding of the discrete-time predator-prey with Allee effect is given. |
| 资助项目 | [National Natural Science Foundation of China] |
| 语种 | 英语 |
| CSCD记录号 | CSCD:4787296 |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/52684]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 作者单位 | 1.中国科学院数学与系统科学研究院 2.湖南师范大学 3.湖南大学 |
| 推荐引用方式 GB/T 7714 | Chen Xianwei,Fu Xiangling,Jing Zhujun. Dynamics in a discrete-time predator-prey system with Allee effect[J]. ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,2013,29(1):143-164. |
| APA | Chen Xianwei,Fu Xiangling,&Jing Zhujun.(2013).Dynamics in a discrete-time predator-prey system with Allee effect.ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,29(1),143-164. |
| MLA | Chen Xianwei,et al."Dynamics in a discrete-time predator-prey system with Allee effect".ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES 29.1(2013):143-164. |
入库方式： OAI收割
来源：数学与系统科学研究院
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