Predator-prey dynamics with square root functional responses. (English) Zbl 1254.92072

Summary: A predator-prey model is considered in which a modified Lotka-Volterra interaction term is used as the functional response of the predator to the prey. The interaction term is proportional to the square root of the prey population, which appropriately models systems in which the prey exhibits strong herd structure implying that the predator generally interacts with the prey along the outer corridor of the herd. Because of the square root term, the solution behavior near the origin is more subtle and interesting than standard models and makes sense ecologically.


92D25 Population dynamics (general)
34C23 Bifurcation theory for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems


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