| Abstract: |
| In this talk, we consider a predator-prey model with prey-dependent search rate in advective environments. We investigate the effect of prey-dependent search rate on model dynamics and provide a complete and explicit classification of global dynamics. Moreover, we show that when the limit cycle is stable, the predator can adjust its search rate to stabilize the positive equilibrium, thereby preventing the paradox of enrichment. Specifically, we employ a new planar analysis method to prove that local stability of the positive equilibrium implies global stability. |
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