Study On Three Kinds Of Population Dynamical Systems And Its Computer Simulation

In this thesis, some theories and approaches related to continuous dynamics, impulsive dynamics, concidence degree theory and numerical simulations are used to investigate dynamical behaviors including the quality of equilibriums, the existence and the uniqueness of the limit cycle;Then, using the theorem of impulsive differentia system, the bounded of the system is given out and the sufficient conditions for the asymptotic stability of the system are obtained;Finally, studing on the prey-predator system with sexual favirtism under impulsive control, with the continuous theorem of concidence degree theory, sufficient condition of existence for periodic solution is given out. The whole thesis is devided into four chapters.The first chaper introduces the historical situation and the present development of relevant subjects about population dynamics as well as the main woke done in this thesis, and gives the main definitions, theorems and lemma about the thesis.In the second chaper, by using of the qualitative theory of ordinary differential equation, the paper considers a class of differential model with the first functional response function under the modify factor, the quality of equilibriums is discussed , the existence and the uniqueness of the limit cycle in this system are proved, Hopf branch theorem are givened out and the limit cycle is obtained, Finally, computer simulations are carried to confirm the main theorems.In the third chaper, this paper studies a predator-prey system with impulsive control, the bounded of the system is given out and the sufficient conditions for the asymptotic stability of the system are obtained. Finally, a model is gived out, and we know that the equilibriums will become stability equilibriums by impulsive control. So we conclude that human and environment can be peaceful coexistence by using appropriate impulsive control.In the fourth chaper, By imposing external influence on the sexual favoritism predator-prey system with periodic coefficients, a predator-prey system with impulsive effects is obtained , and studies the model under impulsive effects. In the biological stocks, the sexual favoritism may lead to sex ratio imbalance, and impact the balance of the biological stocks. So studying the system is becoming very important. In the paper sufficient condition of existence for periodic solution is given out, especially, a sufficient condition of existence for periodic solution of automatic system with impulsive effects is given out...