Impact of physical and behavioral prey refuge on the stability and bifurcation of Gause type Filippov prey-predator system

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• 作者：Debaldev Jana ; Santanu Ray
• 关键词：Discontinuous differential equation ; Filippov solution ; Sliding motion ; Adaptive prey refuge ; Alternative food ; Predator preference
• 刊名：Modeling Earth Systems and Environment
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：2
• 期：1
• 全文大小：884 KB
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• 作者单位：Debaldev Jana (1)
  Santanu Ray (1)
  
  1. Ecological Modelling Laboratory, Department of Zoology, Visva-Bharati University, Santiniketan, 731 235, India
  
• 刊物类别：Earth System Sciences; Math. Appl. in Environmental Science; Statistics for Engineering, Physics, Co
• 刊物主题：Earth System Sciences; Math. Appl. in Environmental Science; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences; Mathematical Applications in the Physical Sciences; Ec
• 出版者：Springer International Publishing
• ISSN：2363-6211

文摘

After the pioneering theoretical studies of Lotka and Volterra, Gause and his co-workers replace the previously used linear functional response by using a saturating functional response with a discontinuity at a threshold prey density. Here we assume that prey density at below this threshold value is effectively and successfully in a refuge patch. In this situation there is no food option for predator and go to extinction. But above this threshold value surplus density of prey is available to predator for its diet. But the system does not show any future activities when prey density is in the vicinity of the threshold density, system is ill posed because the trajectories are not well defined here. In the present study, we redefine and analyze the model by using Filippov regularization method. By this continuation method, the system becomes well posed and gives more results as predicted by Gause. Also predator fully depends upon alternative diet to survive from extinction risk when prey is in refuge patch and system largely varies with the availability of alternative diet resource but in the later case predator again switches to its primary (essential) food. When prey density is in the vicinity of the threshold density, then predator may choose its deit preferentially from essential or alternative resources according to its profit. Numerical examples support these hypothesis and analytical results.