本文關鍵詞：Allee效應對種群動力系統(tǒng)復雜性的影響　出處：《甘肅農業(yè)大學》2015年碩士論文　論文類型：學位論文

  更多相關文章： 捕食-食餌系統(tǒng) Holling-IV型功能反應 收獲努力量 Allee效應 合作進化 平衡態(tài) 數值模擬

【摘要】：近年來,隨著全球環(huán)境破壞的加劇,物種喪失速度隨之加快,資源問題也日益突出,這促使人類對資源的持久利用及可再生資源的循環(huán)利用問題有了深入的考慮,尤其是對生物資源的開發(fā)利用,開發(fā)不當更容易導致物種滅絕。另一方面,大量的實驗研究和野外觀測表明,Allee效應在生態(tài)系統(tǒng)中廣泛存在,瀕危物種更容易受到Allee效應的影響。Allee效應對物種的續(xù)存是潛在的干擾因素,在很大程度上將增加種群局部甚至全局滅絕的可能性。再者,具有Allee效應種群的收獲問題更是敏感,引起生態(tài)學家及保護生物學家的廣泛關注。此外,種群的合作行為的進化是種群進化生物學最重要的理論命題之一,受Allee效應種群的合作行為的進化目前還未引起廣泛的關注。本論文選題于種群動力系統(tǒng)中一致關注的新焦點及未深入涉及的新領域,對其進行了系統(tǒng)地研究。首先詳細討論了Allee效應的提出、演化、以及它在種群動力學系統(tǒng)、單種群模型中的應用;然后基于具有正效應的捕食-食餌系統(tǒng)建立了具有收獲及Allee效應的捕食系統(tǒng);最后,分析了Allee效應對單種群模型中合作行為進化的影響。通過討論其平衡點的存在性和穩(wěn)定性,及數值模擬研究了Allee效應對種群動力系統(tǒng)的影響。研究結果表明:(1)具有Holling-IV型功能反應函數的捕食-食餌動力系統(tǒng)模型,由于捕食正效應較大,兩物種之間會出現周期性振蕩現象(存在極限環(huán));減少捕食正效應,系統(tǒng)就會達到穩(wěn)定的平衡狀態(tài);但若增加系統(tǒng)中食餌種群的環(huán)境容納量,可能由于食餌種群的自然防御功能的增強,導致捕食者種群因食物匱乏而滅絕。(2)對捕食-食餌系統(tǒng)中的食餌種群進行適當地收獲,反而會增加系統(tǒng)的穩(wěn)定性,使得系統(tǒng)更容易達到穩(wěn)定狀態(tài),也會推遲分叉及混沌現象的出現。并應用穩(wěn)定性分析和龐特里亞金極大值原理得出了系統(tǒng)的生物經濟平衡點及最優(yōu)捕獲策略。(3)受強Allee效應影響的系統(tǒng)需更長的時間才能從不穩(wěn)定狀態(tài)到達穩(wěn)定狀態(tài);增加Allee效應,系統(tǒng)出現周期性振蕩現象;繼續(xù)增強Allee效應,食餌種群呈負增長,種群趨向局部滅絕,系統(tǒng)將崩潰;而受弱Allee效應影響時,系統(tǒng)更容易達到平衡態(tài),但會使食餌種群的增長率減少,不過仍保持正值。(4)當進行收獲的捕食-食餌系統(tǒng)受到弱Allee效應的影響,增強弱Allee效應強度,系統(tǒng)出現振蕩現象,且隨著Allee效應強度的增強,系統(tǒng)的振蕩頻率越強。對于原本穩(wěn)定平衡的系統(tǒng),弱Allee效應也會抑制系統(tǒng)達到穩(wěn)定狀態(tài),即達到穩(wěn)定態(tài)需要更長的時間。(5)在惡劣的環(huán)境條件下,Allee效應將導致物種滅絕;在相對優(yōu)越的外部環(huán)境中,Allee效應的存在促進合作行為的進化,且隨著Allee效應強度的增強,更有利于合作行為的入侵,不過過強的Allee效應依舊會導致物種滅絕。
[Abstract]:In recent years, with the intensification of global environmental damage, the rate of species loss has been accelerated, and the problem of resources has become increasingly prominent. This makes us think deeply about the sustainable utilization of resources and the recycling of renewable resources, especially the exploitation and utilization of biological resources. On the other hand, the improper exploitation of biological resources is more likely to lead to species extinction. A large number of experimental studies and field observations show that the Allee effect exists widely in the ecosystem. Endangered species are more vulnerable to the influence of Allee effect. Allee effect is a potential interference factor to the survival of species, to a large extent will increase the possibility of local or even global extinction of the population. The harvesting of populations with Allee effect is more sensitive and has attracted wide attention of ecologists and conservation biologists. The evolution of cooperative behavior of population is one of the most important theoretical propositions in evolutionary biology of population. The evolution of cooperative behavior due to the Allee effect has not attracted much attention. This thesis focuses on the new focus and the new field that has not been deeply involved in the population dynamic system. Firstly, the Allee effect is presented, its evolution and its application in population dynamics system and single population model are discussed in detail. Then, based on the predator-prey system with positive effect, a predator-prey system with harvest and Allee effect is established. Finally, the influence of Allee effect on the evolution of cooperative behavior in a single population model is analyzed, and the existence and stability of the equilibrium point are discussed. The effect of Allee effect on the population dynamic system is studied by numerical simulation. The results show that the predator-prey dynamic system model with Holling-IV type functional response function is obtained. Because of the large positive effect of predation, there will be periodic oscillation between the two species (there is a limit cycle); Reducing the positive predation effect, the system will reach a stable equilibrium state; However, if the environmental capacity of prey population is increased, it may be due to the enhancement of natural defense function of prey population. As a result, the predator population becomes extinct because of lack of food.) the predator population in the predator-prey system can be harvested properly, which will increase the stability of the system and make the system more stable. The bifurcation and chaos will also be delayed. By using the stability analysis and the Ponteriagin maximum principle, the bio-economic equilibrium point and the optimal capture strategy of the system are obtained. It takes a longer time for the system affected by the strong Allee effect to reach the stable state. With the increase of Allee effect, periodic oscillation occurs in the system. If the Allee effect continues to be enhanced, the prey population will increase negatively, the population will tend to become local extinct, and the system will collapse. Under the influence of weak Allee effect, the system is easier to achieve equilibrium state, but will reduce the growth rate of prey population. However, when the prey-prey system is affected by the weak Allee effect, the intensity of the weak Allee effect is enhanced and the system oscillates. The stronger the intensity of Allee effect is, the stronger the oscillation frequency of the system is. For the previously stable system, the weak Allee effect will restrain the system from reaching a stable state. That is to say, it takes a longer time to reach the stable state. (5) the Allee effect will lead to the extinction of species under the harsh environment. In the relatively superior external environment, the existence of Allee effect promotes the evolution of cooperative behavior, and with the increase of the intensity of Allee effect, it is more conducive to the invasion of cooperative behavior. But an excessive Allee effect could still lead to extinction.
【學位授予單位】：甘肅農業(yè)大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O175

【參考文獻】

相關期刊論文 前2條

1 王萬雄;趙燦省;張艷波;;一類具有Allee效應的捕食系統(tǒng)的穩(wěn)定性分析及模擬[J];數學的實踐與認識;2013年20期

2 徐昌進;;具有時滯和Holling Ⅲ型功能反應函數的離散捕食模型的周期解[J];四川師范大學學報(自然科學版);2013年05期

，

本文編號：1429101