| The development of modern science and technology largely depends on theachievements and progresses in physics, chemistry and biology, whose precise de-scription is usually based on appropriate mathematical models. Therefore, itbecomes one of the important directions to study mathematical models arisingfrom applications by using these theories and methods. In this thesis, the sta-bility theory of ordinary diferential equations is used to study several importantbiological mathematical models. The main work is as follows:1. A biological resource harvesting model with price changes is discussed.First, we establish the stability of equilibrium points by the stability theory ofordinary diferential equations. Then, the Poincare map, impulsive diferentialinequality and the methods of qualitative analysis are used to discuss system withimpulse, we prove the existence and the stability of order-1or order-2periodicsolution for this model. Moreover, we show that there is no periodic solution withorder larger than or equal to three. Finally, by analyzing characteristic equation,we study the influence of time delay and obtain some sufcient conditions whichensure the global stability of the equilibrium points of the system. It also showsthat the time delay can cause a stable equilibrium to become unstable.2. We investigate a bioeconomics model with age-structure, impulse andtime delay. It divides this single-population into two structure, namely infancyand adult, we also suggest only adults can be caught. By using comparative theo-rems of impulse diferential equation and the related theories of delay diferentialequation, sufcient conditions which guarantee the global attraction of periodicsolution and permanence of the system are obtained.3. We introduce a discrete fshing model with feedback control and delays.By using comparison principle, sufcient conditions for ensuring the permanenceof the system are obtained. |
