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Effects of prey refuge on a ratio-dependent predator-prey model with stage-structure of prey population. (English) Zbl 1270.35378

Summary: In this paper, a stage-structured predator-prey model is proposed and analyzed to study how the type of refuges used by prey population influences the dynamic behavior of the model. Two types of refuges: those that protect a fixed number of prey and those that protect a constant proportion of prey are considered. Mathematical analyses with regard to positivity, boundedness, equilibria and their stabilities, and bifurcation are carried out. Persistence condition which brings out the useful relationship between prey refuge parameter and maturation time delay is established. Comparing the conclusions obtained from analyzing properties of two types of refuges using by prey, we observe that value of maturation time at which the prey population and hence predator population go extinct is greater in case of refuges which protect a constant proportion of prey.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
91B52 Special types of economic equilibria
92D25 Population dynamics (general)
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