The Diffusive Applications Of Predator-prey Model Over Patches

The diffusive applications of the predator-prey model over different patches are considered in this paper.Some background knowledge, the state of study and the main works of the thesis are introduced in the first chapter.Based on the fact, the diffusive applications of a class of a predator-prey model with Holling II functional response over patches are studied. The attraction domain is found in the first quadrant, that all positive soluions are of strong persistence is proved. If certain conditions are satisfied in the model, the positive equilibrium of the model is local asymptotical stable. The sufficient conditions that a spatial periodic solution of small amplitude is produced in the neighborhood of a positive equilibrium are found in the second chapter.The global and local behaviors of a class of a predator-prey model with Bedding functional response is studied in this passage. That the attraction domain exists in the first quadrant and all positive soluions are of strong persistence are proved. Which the positive equilibrium of the system is local asymptotical stable is given when certain conditions are satisfied in the model in the third chapter, they complete the Zhang Xing-an's result.The diffusive applications of a class of a predator-prey model with harvest and toxicity over patches are studied. The attraction domain is found in the first quadrant. If certain conditions are satisfied in the model, the positive equilibrium of the model is local asymptotical stable and all positive soluions are of strong persistence. The sufficient conditions that a spatial periodic solution of small amplitude is produced in the neighborhood of a positive equilibrium are found in the forth chapter, it completes the Tapasi's result.The model is accessible with example modifying factor in the last chapter.