项目名称: 混沌系统相变触发机制与抗扰稳定性的分数阶表征问题
项目编号: No.11301361
项目类型: 青年科学基金项目
立项/批准年度: 2014
项目学科: 数理科学和化学
项目作者: 邓科
作者单位: 四川大学
项目金额: 22万元
中文摘要: 本项目研究混沌系统的相变触发机制,抗扰稳定性,及其分数阶表征问题。 非线性动力系统关于分岔、混沌的研究近五十年来逐渐进入蓬勃发展期。然而,混沌系统对随机扰动的抑制效应以及触发源对混沌系统的相变诱导等问题的产生机理至今未能厘清,更缺乏严格的数学理论,也使得其应用备受限制。另一方面,分岔、混沌等复杂非线性动力系统中,整体宏观非线性与局部微观复杂性交叉耦合,与不同类型的分数阶性质有着深刻本质联系,因而从分数阶分析学角度对混沌非线性系统进行研究,正是一个自然且可行的进程。 因此,亟待以分数阶分析学角度从数学原理上系统、深入地讨论触发源触发混沌相变的普适条件,随机扰动与系统的类型对抗扰稳定性的影响等关键问题,从而建立混沌相变触发机制与系统抗扰稳定性的数学理论。项目拟研究的内容在理论科学研究前沿以及包括国防高科技在内的工程技术研究领域都有着十分重要且广泛的应用,都是实际需求驱动的数学前沿理论问题。
中文关键词: 分数阶;非线性动力系统;共振;稳定性;
英文摘要: The project study on phase transition trigger mechanism of chaotic system, the stability of disturbance rejection, and its fractional characterization. In recent fifty years, the study of bifurcation and chaotic of nonlinear dynamic system gradually entering the flourishing development period. Howerver, until now the generation mechanism of inhibitory effect to random disturbance of chaotic system and the transformation induced of trigger source to chaotic system is not clear yet. The lack of strict mathematical theory also constrained its application. On the other hand, in the complex nonlinear dynamic system such as bifurcation and chaotic, the whole macroscopic nonlinear and the local microscopic complexity cross coupled, which has the deep and essence relationship of different types of fraction step properties. As a result, it's a natural and feasible process to study chaotic nonlinear system by way of fraction step analysis. Therefore, the key problems such as general condition of how trigger source triggers chaos phase transition and the stability of disturbance rejection effect of the types of random disturbance and system are urgent to be systematically and deeply discussed based on mathematical principle by way of fraction step analysis, and furture more to estanblish the mathematical theory of phas
英文关键词: Fractional-order;Nonlinear dynamic system;Resonance;Stability;