Existence Of Periodic Solutions For Several Classes Of Biological Models

In this paper, by analyzing several specific types of functional response func-tions, we obtain the nature of the monotonic functional response function g(u):(1) g(0) = 0;(2) (dg(u))/(du)> 0,u∈[0,+∞);(3) ,whereδis a positive number.Then combining with the di?usion of eco-system, ratio-dependence and periodicharvest, we establish two kinds of biological models. At last we use nonlinearfunctional analysis methods to respectively prove the existence of periodic solutionsof the models.In chapter two, we generalize a type of predator-prey model with di?usion andspecific functional response. And then we set up a more generalized predator-preymodel basing on di?usion and monotonic functional response as follow: We prove the existence of at least one periodic solution by direct application of theMawhin's theorem.In chapter three, we establish a class of predator-prey model with di?usion,semi-ratio-dependence and periodic harvest as follow, which rarely has been dis-cussed. And we obtain the su?cient condition for the existence of at least two periodicsolutions for the model. At present, there are few literatures discussing the periodic solution for theabstract neutral delay di?erential equations. So in chapter four, by the conetheory, the measure of noncompactness and strict set contraction mapping, theexistence of positive solution for a class of neutral delay di?erential equationsis proved. However, we don't need the conditions: c(t)∈(R,[0,+∞)),τ(t)∈C~2 (R,[0,+∞)) andτ'(t) < 1, which are necessary in the relative literatures.