【作者】 王强；

【导师】 赵洪涌；

【作者基本信息】 南京航空航天大学 ， 应用数学， 2014， 硕士

【摘要】 现代非线性科学的飞速发展，极大的推动了非线性动力学的发展，其中涉及物理学、化学、生物学、生态学、经济金融学等诸多领域。本文主要针对物理化学中的布鲁塞尔子模型和经济学领域中节能减排博弈模型进行系统稳定性研究。在理解模型背景的基础上，运用非线性分析方法，分析模型系统的平衡态，讨论参数（因素）变化对系统平衡态稳定性的影响，并就讨论的结果，对模型进行改进，使其能够更好的接近实际背景。全文内容如下：(1)研究了布鲁塞尔子模型中一个二维非线性反应扩散系统，分析了系统的平衡态的稳定性，给出了系统产生图灵斑图的必要条件，运用多尺度分析法求得系统在图灵分支处的振幅方程。(2)利用文章前面得出的布鲁塞尔子模型的振幅方程，分析系统可能产生的几种斑图，并对每个斑图进行稳定性分析，同时讨论参数变化对斑图稳定性的影响。最后通过数值模拟，验证理论分析的正确性。(3)分析了节能减排管理过程中中央政府、地方政府和企业之间的博弈过程，以收益为基础，运用复制动态方法建立了一般惩罚和动态惩罚机制下的三方博弈模型。进而对模型进行分析，分析其中的演化稳定策略并讨论参数变化对稳定策略的影响，同时运用数值模拟的方法验证结论的正确性。最后，根据讨论的结果，对我国的节能减排提出合理化建议。更多还原

【Abstract】 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.更多还原