本文選題：廣義生物經(jīng)濟(jì)系統(tǒng) + 奇異誘導(dǎo)分岔�。� 參考：《沈陽(yáng)工業(yè)大學(xué)》2015年碩士論文

【摘要】：環(huán)境污染對(duì)生物系統(tǒng)的影響越來(lái)越嚴(yán)重，為了更好地研究物種的發(fā)展和變化規(guī)律，建立生物數(shù)學(xué)模型時(shí)考慮污染因素十分必要。同時(shí)，時(shí)滯也在實(shí)際模型中普遍存在，一個(gè)很小的時(shí)滯可能會(huì)造成系統(tǒng)崩潰，，在考慮受時(shí)滯影響的生物系統(tǒng)時(shí)，則需要進(jìn)一步借助時(shí)滯微分方程來(lái)描述系統(tǒng)。本文主要以廣義系統(tǒng)理論、經(jīng)濟(jì)學(xué)原理、奇異誘導(dǎo)分岔理論、Hopf分岔理論、時(shí)滯系統(tǒng)理論為基礎(chǔ)，對(duì)一類(lèi)污染中的廣義生物經(jīng)濟(jì)系統(tǒng)進(jìn)行了研究。 本文首先介紹了環(huán)境污染給生物種群帶來(lái)的影響，廣義生物系統(tǒng)和時(shí)滯生物系統(tǒng)的研究意義及研究現(xiàn)狀，并由此提出本文所研究問(wèn)題，給出本文所用到的基礎(chǔ)知識(shí)。 其次，建立了受毒素影響的廣義生物經(jīng)濟(jì)模型，利用系統(tǒng)的穩(wěn)定性理論和Routh-hurwitz定理對(duì)系統(tǒng)在平衡點(diǎn)處的穩(wěn)定性進(jìn)行分析，針對(duì)系統(tǒng)的分岔現(xiàn)象設(shè)計(jì)狀態(tài)反饋控制器消除分岔，并使用實(shí)際例子參數(shù)，通過(guò)仿真得到施加控制器后的狀態(tài)響應(yīng)圖，說(shuō)明所得控制器可以對(duì)系統(tǒng)進(jìn)行有效控制。 最后，研究了一類(lèi)受時(shí)滯因素和污染因素影響的廣義生物經(jīng)濟(jì)模型，通過(guò)對(duì)時(shí)滯廣義系統(tǒng)做適當(dāng)?shù)木�性變換，并使用參數(shù)化等方法將時(shí)滯廣義系統(tǒng)轉(zhuǎn)換成一般的時(shí)滯微分系統(tǒng)，對(duì)所得微分時(shí)滯系統(tǒng)在平衡點(diǎn)處的穩(wěn)定性進(jìn)行分析，得出系統(tǒng)在正平衡點(diǎn)處出現(xiàn)Hopf分岔，推導(dǎo)出相關(guān)參數(shù)，說(shuō)明Hopf分岔的穩(wěn)定性和方向性，并通過(guò)數(shù)值仿真驗(yàn)證本文所得結(jié)論的合理性。
[Abstract]:The influence of environmental pollution on biological systems is becoming more and more serious. In order to better study the development and variation of species, it is necessary to consider the pollution factors in the establishment of biological mathematical models. At the same time, time delay also exists in the real model. A small delay may cause the system collapse. When considering the biological system affected by the delay, it is necessary to describe the system with delay differential equation. On the basis of generalized system theory, economic principle, singular induced bifurcation theory, Hopf bifurcation theory and time-delay system theory, a class of generalized bio-economic systems in pollution is studied in this paper. In this paper, the effects of environmental pollution on biological population, the significance and current research status of generalized biological systems and time-delay biological systems are introduced, and the problems and basic knowledge used in this paper are presented. Secondly, the generalized bio-economic model affected by toxin is established. The stability of the system at the equilibrium point is analyzed by using the stability theory of the system and Routh-hurwitz theorem, and the state feedback controller is designed to eliminate the bifurcation for the bifurcation phenomenon of the system. Using the actual example parameters, the state response diagram after applying the controller is obtained by simulation, which shows that the controller can effectively control the system. Finally, a class of generalized bio-economic models affected by time-delay factors and pollution factors are studied. By making appropriate linear transformation to time-delay singular systems and using parameterized methods, the time-delay singular systems are transformed into general time-delay differential systems. The stability of the differential delay system at the equilibrium point is analyzed, and the Hopf bifurcation at the positive equilibrium point is obtained. The related parameters are deduced, and the stability and directivity of the Hopf bifurcation are explained. The rationality of the conclusion is verified by numerical simulation.
【學(xué)位授予單位】：沈陽(yáng)工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類(lèi)號(hào)】：O175;O231

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