發(fā)布時(shí)間：2018-08-20 19:54

【摘要】：隨著社會(huì)的發(fā)展與進(jìn)步，我們所面對(duì)的經(jīng)濟(jì)、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(jì)系統(tǒng)內(nèi)部的非線性，這促使學(xué)者對(duì)復(fù)雜經(jīng)濟(jì)現(xiàn)象背后的非線性規(guī)律的研究，進(jìn)而揭示經(jīng)濟(jì)現(xiàn)象的本質(zhì)，以指導(dǎo)于實(shí)際的經(jīng)濟(jì)活動(dòng)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(jì)學(xué)及其非線性動(dòng)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(jì)理論的研究進(jìn)展，主要包括混沌和分形理論兩個(gè)領(lǐng)域，列舉了經(jīng)濟(jì)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(jì)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(jì)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(diǎn)、鞍點(diǎn)、分岔、Hopf分岔、研究了a,b,c不同組合條件下系統(tǒng)進(jìn)入分岔、混沌的情況下各參數(shù)相互依存變化情況，并對(duì)其全局復(fù)雜性進(jìn)行分析，研究了系統(tǒng)參數(shù)變化所對(duì)應(yīng)的經(jīng)濟(jì)運(yùn)行中的停滯僵化、穩(wěn)定或不穩(wěn)定增長、通貨膨脹、經(jīng)濟(jì)蕭條或經(jīng)濟(jì)局面失控從而導(dǎo)致嚴(yán)重的社會(huì)動(dòng)蕩等的情況； 研究了富有彈性條件下，一類復(fù)雜經(jīng)濟(jì)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?fù)浣Y(jié)構(gòu)演化的參數(shù)臨近值，根據(jù)Taken’s估計(jì)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(shí)間序列復(fù)雜性及不同特性時(shí)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(diǎn)、分岔及Hopf分岔點(diǎn)時(shí)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(shí)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(duì)一類金融系統(tǒng)的內(nèi)在復(fù)雜性進(jìn)行研究，通過數(shù)值模擬，本文發(fā)現(xiàn)了導(dǎo)致系統(tǒng)進(jìn)入混沌的兩條路徑：通往混沌的Ruelle-Takens路徑，以及高階平衡點(diǎn)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(shí)滯參數(shù)τ作為分岔參數(shù)研究了時(shí)滯對(duì)金融系統(tǒng)的影響； 通過一類經(jīng)濟(jì)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(dá)式，研究其實(shí)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(jìn)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(duì)深入分析一類經(jīng)濟(jì)金融系統(tǒng)的內(nèi)部運(yùn)行狀況起到更進(jìn)一步的促進(jìn)作用，提出了系統(tǒng)進(jìn)入混沌的兩條新路徑，為政府制定控制經(jīng)濟(jì)系統(tǒng)的政策提供了依據(jù)，具有實(shí)際的應(yīng)用價(jià)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(jí)別】：博士
【學(xué)位授予年份】：2013
【分類號(hào)】：O415.5;F830

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