BIFURCATION AND CHAOS IN THE TINKERBELL MAP

doi:10.1142/S0218127411030581

CSpace

	BIFURCATION AND CHAOS IN THE TINKERBELL MAP
	Yuan, Shaoliang 3; Jiang, Tao 2; Jing, Zhujun 1
	2011-11-01
发表期刊	INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
ISSN	0218-1274
卷号	21 期号:11 页码:3137-3156
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.
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
语种	英语
资助项目	NNSF of China[11071066]
WOS研究方向	Mathematics ; Science & Technology - Other Topics
WOS类目	Mathematics, Interdisciplinary Applications ; Multidisciplinary Sciences
WOS记录号	WOS:000298815900004
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/11253
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.