Abstract
Taking the spider as a controller of the insects is a very important Green Agricultural Technology. We established a partial differential equation model by adding diffusion term into classical Spider-Insect Model. Using the fixed point index theory, the sufficient condition for the existence of positive solutions is given. Based on the method of parabolic equations, the persistence of positive solution is also studied. Finally, the theoretical results are verified by numerical simulations. Our work shows that intrinsic growth rate of an insect is an important factor that affects its existence and persistence under certain conditions.
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