Dynamic complexities in a Lotka-Volterra predator-prey model concerning impulsive control strategy

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	Dynamic complexities in a Lotka-Volterra predator-prey model concerning impulsive control strategy
	Liu, B ; Zhang, YJ
	2005-02-01
发表期刊	INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
ISSN	0218-1274
卷号	15 期号:2 页码:517-531
摘要	Based on the classical Lotka-Volterra predator-prey system, an impulsive differential equation to model the process of periodically releasing natural enemies and spraying pesticides at different fixed times for pest control is proposed and investigated. It is proved that there exists a globally asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value. Otherwise, the system can be permanent. We observe that our impulsive control strategy is more effective than the classical one if we take chemical control efficiently. Numerical results show that the system we considered has more complex dynamics including period-doubling bifurcation, symmetry-breaking bifurcation, period-halving bifurcation, quasiperiodic oscillation, chaos and nonunique dynamics, meaning that several attractors coexist. Finally, a pest-predator stage-structured model for the pest concerning this kind of impulsive control strategy is proposed, and we also show that there exists a globally asymptotically stable pest-eradication periodic solution when the impulsive period is less than some threshold.
关键词	predator-prey model impulsive perturbation extinction and permanence bifurcation
语种	英语
WOS研究方向	Mathematics ; Science & Technology - Other Topics
WOS类目	Mathematics, Interdisciplinary Applications ; Multidisciplinary Sciences
WOS记录号	WOS:000228906700007
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/2010
专题	中国科学院数学与系统科学研究院
通讯作者	Liu, B
作者单位	1.Xinjiang Univ, Dept Math, Urumqi 830046, Xinjiang, Peoples R China 2.Anshan Normal Univ, Dept Math, Anshan 114005, Liaoning, Peoples R China 3.Acad Math & Syst Sci, Inst Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Liu, B,Zhang, YJ. Dynamic complexities in a Lotka-Volterra predator-prey model concerning impulsive control strategy[J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS,2005,15(2):517-531.
APA	Liu, B,&Zhang, YJ.(2005).Dynamic complexities in a Lotka-Volterra predator-prey model concerning impulsive control strategy.INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS,15(2),517-531.
MLA	Liu, B,et al."Dynamic complexities in a Lotka-Volterra predator-prey model concerning impulsive control strategy".INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 15.2(2005):517-531.