The Study Of A Plant-herbivore Model With Impulse And Toxin-Determined Functional Response

In this paper, we mainly study the dynamics of a plant-herbivore model with impulse and toxin-determined functional response, and consider the the complex case with fixed moments impulse and state impulse respectively. To study these systems has important significance in theory and practice. The article includes three chapters.The preface is in chapter1, we introduce the research background of this article, the main task and some important preliminaries.In Chapter2:the dynamical behavior of a plant-herbivore model with fixed moments impulse and toxin-determined functional response was studied. By using the Floquet multiplier theory of impulsive differential equation and the comparison theorem, we obtained sufficient conditions for global attractivity of periodic solution of the extinction of plants, and the sufficient condition for the permanence of the system. Numerical simulations were carried out to illustrate the main theoretical results.In Chapter3:the dynamical behavior of a plant-herbivore model with state impulse and toxin-determined functional response was studied. When the amount of plants reaches a threshold value Nm, and the number of herbivores is greater than or equal to P*, by the method of artificial capture to control system in order to gain more economic profits. By using the Poincare mapping, analysis of differential inequality and the qualitative theory, we obtain sufficient conditions for the existence and stability of positive order k periodic solutions.