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Nonexistence of nonconstant positive steady states of a diffusive predator-prey model

The authors are supported by the National Natural Science Foundation of China (No.11771109).
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  • In this paper, we investigate a diffusive predator-prey model with a general predator functional response. We show that there exist no nonconstant positive steady states when the interaction between the predator and prey is strong. This result implies that the global bifurcating branches of steady state solutions are bounded loops for a predator-prey model with Holling type Ⅲ functional response.

    Mathematics Subject Classification: Primary:35K57;Secondary:35B36.

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