Stability and global dynamic of a stage-structured predator–prey model with group defense mechanism of the prey

•Dynamics of predator–prey model where the predator feeds on two age classes of prey.•Existence of defense mechanism and the interference of the prey and the age.•The coexistence of the predator and the prey populations is possible.•There exists a bounded range of the carrying capacity for co-existe...

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Bibliographic Details
Published in:	Applied mathematics and computation Vol. 270; pp. 47 - 61
Main Authors:	Falconi, Manuel, Huenchucona, Marcelo, Vidal, Claudio
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01-11-2015
Subjects:	Defense Predator–prey model Prey age structure Switching 70H99 Prey age structure Predator–prey model 58F05 Defense Switching
Online Access:	Get full text
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Summary:	•Dynamics of predator–prey model where the predator feeds on two age classes of prey.•Existence of defense mechanism and the interference of the prey and the age.•The coexistence of the predator and the prey populations is possible.•There exists a bounded range of the carrying capacity for co-existence. In this paper we describe the flow of a predator–prey model where the predator feeds on two age classes of prey. Some basic features of the flow are proved under very mild hypothesis on the functional responses. To study the relationship between the ecological parameters and the behavioral ones, we also analyze a special case of the model where modified versions of the Holling type II functional responses are considered to take into account both a certain interference of the age classes of the prey on the predator activity and a defense mechanism of the juvenile class of the prey. Indeed, we find that independently of the profit that each one of the prey age class provides to the predator, the coexistence of the predator and the prey populations is only possible for a bounded range of the carrying capacity due to the joint action of the defense mechanism and the interference of the prey and the age.
ISSN:	0096-3003 1873-5649
DOI:	10.1016/j.amc.2015.07.109