本文選題：偏利共生 + 相互競爭　； 參考：《信陽師范學(xué)院》2015年碩士論文

【摘要】：在大自然中的無論哪個種群都要受到另一個種群的影響,然而大自然又是復(fù)雜的,有些物種之間不僅僅只存在單一的相互作用.例如,在一定養(yǎng)殖環(huán)境中的黑螞蟻和蚜蟲會為了爭奪生存環(huán)境和資源而相互競爭,然而,蚜蟲在競爭的過程中會產(chǎn)生蜜露,為黑螞蟻的生長提供能量,對自己沒有負(fù)影響,即兩者之間又存在偏利共生的相互作用,也可以稱為單利的相互作用.這種在特定環(huán)境下相互競爭時又單利的模型可以稱為單利相互競爭模型.本文對單利相互競爭模型進行了分析.第一章介紹了本文的引言與預(yù)備知識.第二章首先介紹了沒有時滯的單利相互競爭模型,然后根據(jù)現(xiàn)實情況建立了帶有時滯的單利相互競爭模型,利用連續(xù)動力系統(tǒng)和時滯微分方程基本理論得到了該模型各個平衡點穩(wěn)定性的條件.第三章首先建立了具有脈沖效應(yīng)的單利相互競爭模型,然后利用脈沖微分方程系統(tǒng)的相關(guān)理論證明了此模型解的正性和有界性,并得到了這個系統(tǒng)持久性的充分條件.
[Abstract]:No matter which species in nature is affected by another population, however, nature is complex, some species not only exist a single interaction. For example, black ants and aphids in certain breeding environments will compete with each other for their living environment and resources. However, aphids will produce honeydew in the process of competition, which will provide energy for the growth of black ants and have no negative impact on themselves. That is, there is a symbiotic interaction between the two, also known as simple interest interaction. This kind of model with simple interest when competing with each other in a specific environment can be called the competition model of simple interest. This paper analyzes the competition model of simple interest. The first chapter introduces the introduction and preparatory knowledge of this paper. In the second chapter, we first introduce the model of simple interest competition without time delay, and then establish the model of simple interest competition with time delay according to the actual situation. By using the theory of continuous dynamical system and delay differential equation, the stability conditions of each equilibrium point of the model are obtained. In chapter 3, we first establish a simple interest competition model with impulsive effect, then we prove the positive and boundedness of the solution by using the theory of impulsive differential equation system, and obtain the sufficient condition for the persistence of the model.
【學(xué)位授予單位】：信陽師范學(xué)院
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O175

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