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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.
MSC:
35J55Systems of elliptic equations, boundary value problems (MSC2000)
35B32Bifurcation (PDE)
92C15Developmental biology, pattern formation
92C40Biochemistry, molecular biology
92D25Population dynamics (general)
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