| Abstract: |
| In this talk, we consider the dynamics of a Lotka-Volterra prey-predator model by a class of delay differential equations. The number of prey varies due to a general nonlinear predators` consumption rate with delays. Under the assumption that the consumption rate is monotonically increasing with respect to the number of prey, we theoretically explain that the less effective the predator consume prey or the longer gestation time lag becomes, the numbers of prey and predator tend to oscillate. For the case where the consumption rate is described not only as Holling type I,II but also as Holling type III, we present some ongoing studies. We also mention the difference of the assumptions on the incidence rates appearing in prey-predator models with those in epidemiological models. |
|