DOI: 10.1007/s40974-019-00141-6
论文题名: Dynamical behaviour of a two-prey and one-predator system with help and time delay
作者: Mondal S. ; Samanta G.P.
刊名: Energy, Ecology and Environment
ISSN: 23637692
出版年: 2020
卷: 5, 期: 1 语种: 英语
英文关键词: Discrete delay
; Functional response
; Hopf bifurcation
; Local stability
; Transcritical bifurcations
; Uniform persistence
英文摘要: In this paper, we have investigated a three-species food web model consisting of two preys and one predator with the assumption that in the presence of predator both teams of prey help each other. The interaction between second prey and predator is assumed as a Holling type I (Volterra) functional response because in the absence of any predation, the second prey grows unboundedly following Malthusian law. The relationship between the Canada lynx (Lynx canadensis) and the snowshoe hare (Lepus americanus) can be considered (in good agreement with our model) as an example of how interaction between a predator and its second prey can influence population dynamics. On the other hand, a modified Holling type II functional response is considered to represent the interaction between first prey and predator incorporating the Malthusian law of growth for the second prey. Also, there is no inter-specific competition among the two-prey species as the second prey has sufficient resources. Moreover, it is assumed that there may be competition among the individuals of the predator species. Next, we have discussed the positivity of the solutions of the proposed system. In this work, we have studied about various types of equilibrium points and their stability behaviour. Also, transcritical bifurcations of the planer equilibrium points and persistent of system are discussed. The effect of discrete time delay (as gestation period) is analysed to observe the switching behaviour of the delay parameter. The maximum length of delay has been determined to preserve the stability of one-periodic limit cycle. Also, the direction, period and the stability of bifurcating periodic solutions have been examined based on normal form method and centre manifold theory. Numerical simulations are also performed to verify analytical findings. © 2019, The Joint Center on Global Change and Earth System Science of the University of Maryland and Beijing Normal University. Citation statistics:
资源类型: 期刊论文
标识符: http://119.78.100.158/handle/2HF3EXSE/159840
Appears in Collections: 气候变化与战略
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作者单位: Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, 711103, India
Recommended Citation:
Mondal S.,Samanta G.P.. Dynamical behaviour of a two-prey and one-predator system with help and time delay[J]. Energy, Ecology and Environment,2020-01-01,5(1)