Complex Dynamics in a Discrete-time Predator-prey System without Allee Effect

CSpace

	Complex Dynamics in a Discrete-time Predator-prey System without Allee Effect
其他题名	Complex Dynamics in a Discrete-time Predator-prey System without Allee Effect
	Chen Xianwei 1; Fu Xiangling 1; Jing ZhuJun 2
	2013
发表期刊	ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
ISSN	0168-9673
卷号	29 期号:2 页码:355-376
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.
其他摘要	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 perioddoubling 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.
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
收录类别	CSCD
语种	英语
资助项目	[National Natural Science Foundation of China]
CSCD记录号	CSCD:4800940
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/57031
专题	中国科学院数学与系统科学研究院
作者单位	1.湖南大学 2.湖南师范大学 3.中国科学院数学与系统科学研究院
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.