Study On Mathematical Models Of Pinus Koraiensis With Time Delay

Pinus Koraiensis(Korean pine) is one of the important and dominant tree species in the Northeast region of China. The value of Pine species is not only reflected in protecting ecological environment, but also in economic terms. Therefore, the study of pine ecosystem is of great significance, Newborn pups regard the maternal milk as the whole source of nutritional needs. So lactating female squirrels will increase the intensity of predation to pine seeds, and so the number of pine seeds buried in the soil increases. At the same time, the probability of loss of pine increases, and probability which Pine seeds become germination will increase in the suitable environment. Therefore, it is necessary to take lactation of squirrels into account, so that the dynamic mathematical model reflects the interaction between the three realistically.This paper considers the actual lactation of squirrels phenomenon, the establishment of a delay differential Pine mathematical model describes the relationship between reflection of pine seeds, squirrels and seedlings with the population of linear and nonlinear.This paper studys four types of the population of Pinus Koraiensis models with time delay. Study on dynamic behavior of the model with theoretical knowledge of delay differential, Numerical simulations of pine seeds, squirrels and seedlings show trend about delays parameters which are on behalf of the lactation of squirrels. The conclusions show the impact of delay parameters on the three-cycle stability characteristics. In this paper, the conclusions indicate that pine seeds, squirrels and seedlings of natural Korean pine forest can form a mutual growth and decline over time and regular cyclical shocks under certain conditions, and they ultimately maintain dynamic stability.The whole paper is divided into five chapters. The first chapter is an introduction which elaborates the research background of this paper, the purpose and significance of the study, the situation of current research in the Population of Pinus Koraiensis, the main content of this paper and some prior knowledge required by the problem of this paper. Chapter II constructed a model of linear time-delay about the Population of Pinus Koraiensis with delay parameter that is lactation of squirrels. First, the stability of the positive equilibrium is analyzed and determined, then this paper gived the time delay boundaries and export existence condition of Hopf bifurcation.The third chapter constructed the two nonlinear the Population of Pinus Koraiensis with delay parameter. First, the stability of the positive equilibrium is analyzed and determined, then this paper obtained Hopf bifurcation direction and Formula for calculating the stabilityof bifurcating periodic solutions. The fourth chapter constructed a model with artificial linear time-delay population of Pinus Koraiensis. First, the stability of the positive equilibrium is analyzed and determined, then this paper gave the time delay boundaries and export existence condition of Hopf bifurcation. Chapter five concludes the main conclusions and outlook of this article.