Complex Dynamics in a Discrete-time Predator-prey System without Allee Effect
文献类型：期刊论文
| 作者 | Chen Xianwei2; Fu Xiangling2; Jing ZhuJun3 |
| 刊名 | ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
 |
| 出版日期 | 2013 |
| 卷号 | 29期号:2页码:355-376 |
| ISSN号 | 0168-9673 |
| 关键词 | STATE-FEEDBACK CONTROL DELAYS CHAOS MODEL BIFURCATION BEHAVIORS STABILITY CYCLES predator-prey system flip bifurcation Hopf bifurcation Marotto's chaos transient chaos |
| 其他题名 | Complex Dynamics in a Discrete-time Predator-prey System without Allee Effect |
| 英文摘要 | In this paper, complex dynamics of the discrete-time predator-prey system without Allee effect are investigated in detail. Conditions of the existence for flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory and checked up by numerical simulations. Chaos, in the sense of Marotto, is also proved by both analytical and numerical methods. Numerical simulations included bifurcation diagrams, Lyapunov exponents, phase portraits, fractal dimensions display new and richer dynamics behaviors. More specifically, this paper presents the finding of period-one orbit, period-three orbits, and chaos in the sense of Marotto, complete period-doubling bifurcation and invariant circle leading to chaos with a great abundance period-windows, simultaneous occurrance of two different routes (invariant circle and inverse period-oubling bifurcation, and period-doubling bifurcation and inverse period-doubling bifurcation) to chaos for a given bifurcation parameter, period doubling bifurcation with period-three orbits to chaos, suddenly appearing or disappearing chaos, different kind of interior crisis, nice chaotic attractors, coexisting (2,3,4) chaotic sets, non-attracting chaotic set, and so on, in the discrete-time predator-prey system. Combining the existing results in the current literature with the new results reported in this paper, a more complete understanding is given of the discrete-time predator-prey systems with Allee effect and without Allee effect. |
| 资助项目 | [National Natural Science Foundation of China] |
| 语种 | 英语 |
| CSCD记录号 | CSCD:4800940 |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/57030]  |
| 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.湖南大学 3.湖南师范大学 |
| 推荐引用方式 GB/T 7714 | Chen Xianwei,Fu Xiangling,Jing ZhuJun. Complex Dynamics in a Discrete-time Predator-prey System without Allee Effect[J]. ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,2013,29(2):355-376. |
| APA | Chen Xianwei,Fu Xiangling,&Jing ZhuJun.(2013).Complex Dynamics in a Discrete-time Predator-prey System without Allee Effect.ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,29(2),355-376. |
| MLA | Chen Xianwei,et al."Complex Dynamics in a Discrete-time Predator-prey System without Allee Effect".ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES 29.2(2013):355-376. |
入库方式： OAI收割
来源：数学与系统科学研究院
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