Bifurcation and chaos in neural excitable system

doi:10.1016/j.choas.2005.04.060

CSpace

	Bifurcation and chaos in neural excitable system
	Jing, ZJ ; Yang, JP ; Feng, W
	2006
发表期刊	CHAOS SOLITONS & FRACTALS
ISSN	0960-0779
卷号	27 期号:1 页码:197-215
摘要	In this paper, we investigate the dynamical behaviors of neural excitable system without periodic external current (proposed by Chialvo [Generic excitable dynamics on a two-dimensional map. Chaos, Solitons & Fractals 1995;5(3-4):46179] and with periodic external current as system's parameters vary. The existence and stability of three fixed points, bifurcation of fixed points, the conditions of existences of fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using bifurcation theory and center manifold theorem. The chaotic existence in the sense of Marotto's definition of chaos is proved. We then give the numerical simulated results (using bifurcation diagrams, computations of Maximum Lyapunov exponent and phase portraits), which not only show the consistence with the analytic results but also display new and interesting dynamical behaviors, including the complete period-doubling and inverse period-doubling bifurcation, symmetry period-doubling bifurcations of period-3 orbit, simultaneous occurrence of two different routes (invariant cycle and period-doubling bifurcations) to chaos for a given bifurcation parameter, sudden disappearance of chaos at one critical point, a great abundance of period windows (period 2 to 10, 12, 19, 20 orbits, and so on) in transient chaotic regions with interior crises, strange chaotic attractors and strange non-chaotic attractor. In particular, the parameter k plays a important role in the system, which can leave the chaotic behavior or the quasi-periodic behavior to period-1 orbit as k varies, and it can be considered as an control strategy of chaos by adjusting the parameter k. Combining the existing results in [Generic excitable dynamics on a two-dimensional map. Chaos, Solitons & Fractals 1995;5(3-4):461-79] with the new results reported in this paper, a more complete description of the system is now obtained. (c) 2005 Elsevier Ltd. All rights reserved.
DOI	10.1016/j.choas.2005.04.060
语种	英语
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Interdisciplinary Applications ; Physics, Multidisciplinary ; Physics, Mathematical
WOS记录号	WOS:000232094700022
出版者	PERGAMON-ELSEVIER SCIENCE 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/3393
专题	中国科学院数学与系统科学研究院
通讯作者	Jing, ZJ
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China 2.Hunan Normal Univ, Dept Math, Changsha 410081, Peoples R China 3.Beihang Univ, Dept Math, Beijing 100083, Peoples R China 4.Chinese Acad Sci, Grad Sch, Beijing 100039, Peoples R China
推荐引用方式 GB/T 7714	Jing, ZJ,Yang, JP,Feng, W. Bifurcation and chaos in neural excitable system[J]. CHAOS SOLITONS & FRACTALS,2006,27(1):197-215.
APA	Jing, ZJ,Yang, JP,&Feng, W.(2006).Bifurcation and chaos in neural excitable system.CHAOS SOLITONS & FRACTALS,27(1),197-215.
MLA	Jing, ZJ,et al."Bifurcation and chaos in neural excitable system".CHAOS SOLITONS & FRACTALS 27.1(2006):197-215.