| Abstract: |
| Coexistence and seasonal fluctuations of predator and prey populations are common and well documented in ecology. In this talk, I will present a new predator-prey model that incorporates seasonality and predator maturation delay simultaneously. Both seasonality and time delay have been known as the main culprits for driving population cycles in addition to predator-prey interactions. We theoretically obtain the threshold result in terms of $R_0$ for the coexistence of predator and prey populations in a seasonally changing environment. We numerically explore the roles of seasonality, {\it Daphnia} maturation delay and {\it Daphnia}-algae interaction in determining seasonal {\it Daphnia}-algae cycles. The analytic method presented in this talk can be employed to prove the uniform persistence of many other periodic delay differential equations. The numerical results may help the study of algae blooms and the preservation of zooplankton in coastal areas. To our knowledge, this work is the first one that carries out sensitivity analysis of $R_0$ for a periodic system with time delay. This talk is based on a joint work with Hao Wang and Michael Li. |
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