The Complexity Of A Nonlinear Business Cycle Model

The economic system is an open complex system. With the deeping of global economy integration, the factors affecting the economy and relations of the factors become more complex and the traditional economic theory is insufficient to study business cycle. With the development of nonlinear science, nonlinear economics is becoming the research focus of modern economics and has made great progress. This dissertation studies the complex nonlinear phenomenon in a business cycle model based on the theory of modern nonlinear dynamics. Also, the empirical analysis with the example of Tianjin is provided. The main content is as follows:1. A nonlinear business cycle model in resonance is studied via the theory of nonlinear dynamical system. The first and second order approximate solutions and relation between the swing and phase of the second order approximate solutions are analyzed. The swing of extrinsic motivation, frequency of the approximate solutions besides the relations among them and the damping parameters are also analyzed. In addition, the periodic solutions, the approximate period solutions of the system and the access to bifurcation and chaos are revealed.2. The nonlinear business cycle model in oscillation condition and off-resonance is studied. The first and second order approximate solutions of the system are obtained via the method of multiple scales, the relations among the swing, phase, damping parameters, and driving frequency of the first order approximate solutions are provided. The overall evolution of the system solutions with the varying of the force is also revealed. The access of the system to mutation, fuzzy field and chaos and the evolvement of the business cycle model are discussed in detail.3. The nonlinear business cycle model in super-harmonic resonance is studied. The first order approximate solutions of the system, the relations among the swing, phase, damping parameters, driving amplitude and driving frequency are discussed. The complex evolutionary process of the system is explored via the condition of the interdependence of the parameters.4. Helical calendar is introduced, and the relationship between the business cycle and helical calendar is studied with the empirical analysis of Tianjin to provide effective basis for finding the discipline of business cycle.