基于復(fù)雜性理論的經(jīng)濟系統(tǒng)Hopf分岔及其應(yīng)用研究
發(fā)布時間：2018-08-20 19:54
【摘要】：隨著社會的發(fā)展與進步，我們所面對的經(jīng)濟、金融系統(tǒng)越來越復(fù)雜，而導(dǎo)致這種復(fù)雜性的根源就是經(jīng)濟系統(tǒng)內(nèi)部的非線性，這促使學(xué)者對復(fù)雜經(jīng)濟現(xiàn)象背后的非線性規(guī)律的研究，進而揭示經(jīng)濟現(xiàn)象的本質(zhì)，以指導(dǎo)于實際的經(jīng)濟活動中。 本文在學(xué)者們研究工作的基礎(chǔ)上，采用管理學(xué)、經(jīng)濟學(xué)及其非線性動力系統(tǒng)的理論和方法，做了以下方面的工作： 論文首先綜述了非線性經(jīng)濟理論的研究進展，主要包括混沌和分形理論兩個領(lǐng)域，列舉了經(jīng)濟中重要的非線性模型，深入介紹了混沌、分形兩大經(jīng)典非線性理論在經(jīng)濟領(lǐng)域的應(yīng)用； 在國內(nèi)外學(xué)者研究工作的基礎(chǔ)上，研究了一類經(jīng)濟金融系統(tǒng)不同參數(shù)組合條件下的一系列非線性特性包括：穩(wěn)定結(jié)點、鞍點、分岔、Hopf分岔、研究了a,b,c不同組合條件下系統(tǒng)進入分岔、混沌的情況下各參數(shù)相互依存變化情況，并對其全局復(fù)雜性進行分析，研究了系統(tǒng)參數(shù)變化所對應(yīng)的經(jīng)濟運行中的停滯僵化、穩(wěn)定或不穩(wěn)定增長、通貨膨脹、經(jīng)濟蕭條或經(jīng)濟局面失控從而導(dǎo)致嚴重的社會動蕩等的情況； 研究了富有彈性條件下，一類復(fù)雜經(jīng)濟系統(tǒng)的Hopf分岔，分岔發(fā)生的參數(shù)演化條件，，研究了Hopf分岔前出現(xiàn)的周期軌道的穩(wěn)定性問題，并依次研究了系統(tǒng)拓撲結(jié)構(gòu)演化的參數(shù)臨近值，根據(jù)Taken’s估計研究了上述各種情況下，系統(tǒng)的內(nèi)在復(fù)雜性的演化情況；應(yīng)用復(fù)原圖(RP)和相干復(fù)原圖(CRP)方法，結(jié)合復(fù)雜度分析的ApEn算法，研究了時間序列復(fù)雜性及不同特性時序數(shù)據(jù)的復(fù)原圖和相干復(fù)原圖上的特性，研究了Lorenz系統(tǒng)、穩(wěn)定的匯、鞍點、分岔及Hopf分岔點時序數(shù)據(jù)的復(fù)原圖和相干復(fù)原圖，并研究了其相應(yīng)的時序數(shù)據(jù)的復(fù)雜度，得到了五種新的復(fù)原圖和相干復(fù)原圖； 對一類金融系統(tǒng)的內(nèi)在復(fù)雜性進行研究，通過數(shù)值模擬，本文發(fā)現(xiàn)了導(dǎo)致系統(tǒng)進入混沌的兩條路徑：通往混沌的Ruelle-Takens路徑，以及高階平衡點分岔接倍周期分岔通向混沌，并在此過程中產(chǎn)生了奇異非混沌吸引子(SNA)；之后采用了時滯參數(shù)τ作為分岔參數(shù)研究了時滯對金融系統(tǒng)的影響； 通過一類經(jīng)濟系統(tǒng)的雅克比矩陣的變化推導(dǎo)出了系統(tǒng)Lyapunov指數(shù)的數(shù)學(xué)表達式，研究其實部隨著參數(shù)a,b,c的變化的情況，研究了不同參數(shù)組合條件下系統(tǒng)進入分岔、混沌的道路，為系統(tǒng)的混沌控制奠定基礎(chǔ)。 本文的研究成果將對深入分析一類經(jīng)濟金融系統(tǒng)的內(nèi)部運行狀況起到更進一步的促進作用，提出了系統(tǒng)進入混沌的兩條新路徑，為政府制定控制經(jīng)濟系統(tǒng)的政策提供了依據(jù)，具有實際的應(yīng)用價值。
[Abstract]:With the development and progress of society, the economic and financial system we face is becoming more and more complex, and the source of this complexity is the nonlinearity within the economic system. This urges scholars to study the nonlinear laws behind complex economic phenomena, and then to reveal the essence of economic phenomena, in order to guide the actual economic activities. Based on the research work of scholars, this paper uses the theories and methods of management, economics and nonlinear dynamic systems to do the following work: firstly, this paper summarizes the research progress of nonlinear economic theory. This paper mainly includes two fields: chaos and fractal theory, enumerates the important nonlinear models in economy, and introduces the application of chaos and fractal in the economic field. Based on the research work of scholars at home and abroad, a series of nonlinear characteristics of a class of economic and financial systems with different parameter combinations are studied, including stable node, saddle point, bifurcation and Hopf bifurcation. In this paper, the variation of the interdependence of the system parameters under the condition of bifurcation and chaos is studied, and the global complexity is analyzed. The stagnation and fossilization in the economic operation corresponding to the variation of the system parameters are studied. Stable or unstable growth, inflation, economic depression or runaway economic situation leading to serious social unrest, etc.; the Hopf bifurcation of a class of complex economic systems under elastic conditions is studied. The parameter evolution condition of bifurcation, the stability of periodic orbit before Hopf bifurcation is studied, and the parameter approaching value of topological evolution of system is studied in turn. According to the Taken's estimation, the above conditions are studied. The evolution of the inherent complexity of the system is studied by using the restoration graph (RP) and coherent restoration graph (CRP) methods, combined with the ApEn algorithm of complexity analysis, and the characteristics of the restoration graph and coherent restoration graph of time series complexity and time series data with different characteristics are studied. In this paper, the restoration diagram and coherent restoration diagram of Lorenz system, stable convergence, saddle point, bifurcation and Hopf bifurcation data are studied. The complexity of the corresponding time series data is studied, and five kinds of new restoration graphs and coherent restoration graphs are obtained. The intrinsic complexity of a class of financial systems is studied. By numerical simulation, two paths leading to chaos are found: the Ruelle-Takens path to chaos. The bifurcation of higher order equilibrium points leads to chaos, and the singular nonchaotic attractor (SNA);) is produced in the process. The delay parameter 蟿 is used as the bifurcation parameter to study the influence of time delay on the financial system. The mathematical expression of Lyapunov exponent is derived from the change of Jacobian matrix of a class of economic systems. The change of system Lyapunov exponent with the change of parameter a / b / c is studied, and the bifurcation of the system is studied under the condition of different combination of parameters. The road of chaos lays the foundation for the chaos control of the system. The research results of this paper will further promote the analysis of the internal operation of a kind of economic and financial system, and bring forward two new ways for the system to enter chaos, which provides the basis for the government to formulate the policy of controlling the economic system. It has practical application value.
【學(xué)位授予單位】：天津大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2013
【分類號】：O415.5;F830
本文編號：2194807
[Abstract]:With the development and progress of society, the economic and financial system we face is becoming more and more complex, and the source of this complexity is the nonlinearity within the economic system. This urges scholars to study the nonlinear laws behind complex economic phenomena, and then to reveal the essence of economic phenomena, in order to guide the actual economic activities. Based on the research work of scholars, this paper uses the theories and methods of management, economics and nonlinear dynamic systems to do the following work: firstly, this paper summarizes the research progress of nonlinear economic theory. This paper mainly includes two fields: chaos and fractal theory, enumerates the important nonlinear models in economy, and introduces the application of chaos and fractal in the economic field. Based on the research work of scholars at home and abroad, a series of nonlinear characteristics of a class of economic and financial systems with different parameter combinations are studied, including stable node, saddle point, bifurcation and Hopf bifurcation. In this paper, the variation of the interdependence of the system parameters under the condition of bifurcation and chaos is studied, and the global complexity is analyzed. The stagnation and fossilization in the economic operation corresponding to the variation of the system parameters are studied. Stable or unstable growth, inflation, economic depression or runaway economic situation leading to serious social unrest, etc.; the Hopf bifurcation of a class of complex economic systems under elastic conditions is studied. The parameter evolution condition of bifurcation, the stability of periodic orbit before Hopf bifurcation is studied, and the parameter approaching value of topological evolution of system is studied in turn. According to the Taken's estimation, the above conditions are studied. The evolution of the inherent complexity of the system is studied by using the restoration graph (RP) and coherent restoration graph (CRP) methods, combined with the ApEn algorithm of complexity analysis, and the characteristics of the restoration graph and coherent restoration graph of time series complexity and time series data with different characteristics are studied. In this paper, the restoration diagram and coherent restoration diagram of Lorenz system, stable convergence, saddle point, bifurcation and Hopf bifurcation data are studied. The complexity of the corresponding time series data is studied, and five kinds of new restoration graphs and coherent restoration graphs are obtained. The intrinsic complexity of a class of financial systems is studied. By numerical simulation, two paths leading to chaos are found: the Ruelle-Takens path to chaos. The bifurcation of higher order equilibrium points leads to chaos, and the singular nonchaotic attractor (SNA);) is produced in the process. The delay parameter 蟿 is used as the bifurcation parameter to study the influence of time delay on the financial system. The mathematical expression of Lyapunov exponent is derived from the change of Jacobian matrix of a class of economic systems. The change of system Lyapunov exponent with the change of parameter a / b / c is studied, and the bifurcation of the system is studied under the condition of different combination of parameters. The road of chaos lays the foundation for the chaos control of the system. The research results of this paper will further promote the analysis of the internal operation of a kind of economic and financial system, and bring forward two new ways for the system to enter chaos, which provides the basis for the government to formulate the policy of controlling the economic system. It has practical application value.
【學(xué)位授予單位】：天津大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2013
【分類號】：O415.5;F830
【參考文獻】
相關(guān)期刊論文 前10條
1 張曉丹,李志萍,張麗麗;一類基于奇異值分解的Lyapunov指數(shù)計算方法[J];北京科技大學(xué)學(xué)報;2005年03期
2 張玲;;一類混沌金融系統(tǒng)的自適應(yīng)反饋同步研究[J];赤峰學(xué)院學(xué)報(自然科學(xué)版);2008年07期
3 羅珉,李映東;混沌理論對管理學(xué)發(fā)展的啟示[J];財經(jīng)科學(xué);2004年06期
4 周孝華;李尚南;;一類金融混沌系統(tǒng)的控制方法[J];財經(jīng)論叢;2007年03期
5 莊新田;李冰;;對有效市場的挑戰(zhàn)——資本市場分形與混沌的研究綜述[J];東北大學(xué)學(xué)報(社會科學(xué)版);2008年02期
6 楊洪明;譚韜;孟憲志;;電力市場古諾動態(tài)博弈的時滯反饋混沌控制[J];電力系統(tǒng)及其自動化學(xué)報;2010年01期
7 張守一,葛新權(quán);對經(jīng)濟混沌的初步分析[J];大自然探索;1992年03期
8 劉曉君;李險峰;;時滯反饋法控制一個自治混沌系統(tǒng)[J];河北師范大學(xué)學(xué)報(自然科學(xué)版);2008年02期
9 朱曉華,毛建明;經(jīng)濟混沌研究的非線性科學(xué)方法[J];經(jīng)濟地理;2000年02期
10 彭志忠,張文杰;經(jīng)濟管理學(xué)領(lǐng)域中非線性科學(xué)理論應(yīng)用研究[J];經(jīng)濟師;2001年05期
本文編號：2194807
本文鏈接：http://sikaile.net/guanlilunwen/bankxd/2194807.html
最近更新
教材專著
