Study On Dynamics Of The Impulsive Plant-herbivore Model With Plant Toxicity

The interaction between herbivores and plants is one of the most basic nutritional rela-tionships in nature and ecosystem.Some plants can release some chemical toxins to resist herbivores,which makes the traditional predator-prey model unable to accurately describe the interaction between these plants and herbivores.This phenomenon is called plant tox-icity effect between plants and herbivores.In order to describe this effect more accurately,Professor Feng Zhilan of Purdue University and Ecologist Donald DeAngelis proposed one new functional response function called toxin-determined functional response.Up to now,the research work on this new functional response has mainly been carried out in a contin-uous system.In this thesis,we considered two classes of impulsive plant-herbivore model with toxin-determined functional response.This thesis is divided into five chapters.In Chapter 1,we firstly introduce the back-ground of the problems and the related works in China and abroad,and then we state the problem studied and outlines of this thesis.The preliminary knowledge is given in Chapter 2.After,Chapters 3 and 4 are devoted to studying the dynamical behavior of solutions to the following problemHere D{x,y)=B(x,y)(1-B(x,y)/4G).In the third chapter,we consider the existence,local and global stability of trivial periodic solutions when B{x,y)is the Holling-II functional response function,i.e.B{x,y)=x/1+hcx.Later,in the fourth chapter,we consider the case B(x,y)=x/1+hcx+?y in Problem(E).Our main results are also about the existence,local and global asymptotic behavior of the trivial solutions.At the last chapter of this thesis,we mainly summary our results and give a further interesting problems.