Research On Dynamics Of Two Nonlinear Systems

The rapid development of modern nonlinear science, greatly promoted the development ofnonlinear dynamics, which involves many fields, such as physics, chemistry, biology, ecology,economics and finance. This article focused on the stability analysis of Brusselator model inphysical-chemistry and evolution game system based on the energy-saving in economics. On the basisof understanding the models, using nonlinear analysis methods to study the stability of the models,discuss the impact of parameters (factors) changing on the stability of the equilibrium state of thesystem. Accoding to the outcome, we improve the models so that it could be better close to the actualbackground.The main contents in this dissertation can be stated as follows:(1) A two-dimensional nonlinear reaction-diffusion system of Brusselators is investigated. Weanalyze the stability of the equilibrium state of the system, give the necessary conditions ofthe system to generate the Turing patterns, obtain the amplitude equations at the Turingbifurcation point by using multi-scale analysis(2) Using the amplitude equations of Brusselators obtained in front part of this article, analyzethe several patterns that the system may generate and the stability of each. Then, we discussthe impact of parameters changing to the stability of the patterns. Finally, we verify theresults obtained by the front via the numerical simulation.(3) In the third part, we study the game behavior among central government, local government,and enterprises in the energy conservation management process. Based on the revenue, wedevelop the general punishment and dynamic punishment models by replicator dynamicmethod, analyze these models, discuss the evolutionary stable strategy and the impact ofparameters changing on the stable strategy. Meantime, we verify the result by numericalsimulation. Finally, according to the outcome of the discussion, some reasonable proposalsare gived to China’s energy saving.