Study On Predator - Prey Model With Time - Delay And Ratio - Based

More and more biologists and mathematicians have considered biological systems by maths model. In real life, they have been widely used. The chaos in biological systems is investigated by many authors. Some systems has not been analysised in-depth.From the view of human’s practical needs, a ratio-dependent model with time de-layed harvesting is discussed in Chapter 2. By the Hopf bifurcation theory, we choose the delay as bifurcation parameter and find that when the delay passes through the critical value, the stability of positive equilibrium changes and bifurcates a family of periodic orbits. By numerical simulation, chaos can be observed. In Chapter 3, we analysis a three species ratio-dependent food chain system with time delayed harvest-ing. Similarly, we take the delay as the bifurcation parameter and find that when the delay passes through the critical value, the positive equilibrium changes from stable to unstable. On some parameters periodic solutions appear, chaos can be observed. Finally a numerical simulation is given to support our results.