BIFURCATION AND CHAOS IN THE TINKERBELL MAP
文献类型：期刊论文
| 作者 | Yuan, Shaoliang3; Jiang, Tao2; Jing, Zhujun1 |
| 刊名 | INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
 |
| 出版日期 | 2011-11-01 |
| 卷号 | 21期号:11页码:3137-3156 |
| ISSN号 | 0218-1274 |
| 关键词 | Tinkerbell map fold bifurcation flip bifurcation Hopf bifurcation chaos in the sense of Marotto transient chaos invariant circle periodic window |
| DOI | 10.1142/S0218127411030581 |
| 英文摘要 | In this paper, the dynamical behaviors of the Tinkerbell map are investigated in detail. Conditions for the existence of fold bifurcation, flip bifurcation and Hopf bifurcation are derived, and chaos in the sense of Marotto is verified by both analytical and numerical methods. Numerical simulations include bifurcation diagrams in two-and three-dimensional spaces, phase portraits, and the maximum Lyapunov exponent and fractal dimension, as well as the distribution of dynamics in the parameter plane, which exhibit new and interesting dynamical behaviors. More specifically, this paper reports the findings of chaos in the sense of Marotto, a route from an invariant circle to transient chaos with a great abundance of periodic windows, including period-2, 7, 8, 9, 10, 13, 17, 19, 23, 26 and so on, and suddenly appearing or disappearing chaos, convergence of an invariant circle to a period-one orbit, symmetry-breaking of periodic orbits, interlocking period-doubling bifurcations in chaotic regions, interior crisis, chaotic attractors, coexisting (2, 10, 13) chaotic sets, two coexisting invariant circles, two attracting chaotic sets coexisting with a non-attracting chaotic set, and so on, all in the Tinkerbell map. In particular, it is found that there is no obvious road from period-doubling bifurcations to chaos, but there is a route from a period-one orbit to an invariant circle and then to transient chaos as the parameters are varied. Combining the existing results in the current literature with the new results reported in this paper, a more complete understanding of the Tinkerbell map is obtained. |
| 资助项目 | NNSF of China[11071066] |
| WOS研究方向 | Mathematics ; Science & Technology - Other Topics |
| 语种 | 英语 |
| 出版者 | WORLD SCIENTIFIC PUBL CO PTE LTD |
| WOS记录号 | WOS:000298815900004 |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/11252]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Jing, Zhujun |
| 作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, Ctr Dynam Syst, Beijing 100190, Peoples R China 2.Beijing WuZi Univ, Informat Sch, Beijing 101149, Peoples R China 3.Hunan Normal Univ, Coll Math & Comp Sci, Changsha 410081, Hunan, Peoples R China |
| 推荐引用方式 GB/T 7714 | Yuan, Shaoliang,Jiang, Tao,Jing, Zhujun. BIFURCATION AND CHAOS IN THE TINKERBELL MAP[J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS,2011,21(11):3137-3156. |
| APA | Yuan, Shaoliang,Jiang, Tao,&Jing, Zhujun.(2011).BIFURCATION AND CHAOS IN THE TINKERBELL MAP.INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS,21(11),3137-3156. |
| MLA | Yuan, Shaoliang,et al."BIFURCATION AND CHAOS IN THE TINKERBELL MAP".INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 21.11(2011):3137-3156. |
入库方式： OAI收割
来源：数学与系统科学研究院
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