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Non-existence of non-constant positive steady states of two Holling type-II predator-prey systems: strong interaction case. (English) Zbl 1169.35328
Summary: We prove the non-existence of non-constant positive steady state solutions of two reaction-diffusion predator-prey models with Holling type-II functional response when the interaction between the predator and the prey is strong. The result implies that the global bifurcating branches of steady state solutions are bounded loops.
35J55Systems of elliptic equations, boundary value problems (MSC2000)
35B32Bifurcation (PDE)
92C15Developmental biology, pattern formation
92C40Biochemistry, molecular biology
92D25Population dynamics (general)
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