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在点映射和延拓法基础上,提出一种适于求解慢变参数非线性动力系统分叉混沌问题的新算法-映射延拓综合法。用本方法对含慢变参数的杜芬方程试算,绘制稳态解随参数变化的准稳态解图,分析了解随参数变化的演化规律。与多初值点映射法相比,它具有计算精度高、速度快、分析处理方便等优点;新算法更适于作高维慢变参数非线性系统振动特性的研究。  相似文献   
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裂纹转子分岔、混沌行为研究   总被引:8,自引:0,他引:8  
分析非线性涡动中裂纹转子在裂纹存在和裂纹扩展两种情形下的典型非线性动力学行为--混沌和分岔现象。在2/3倍临界转速区,裂纹深度浅于R/2的裂纹转子有分岔和拟周期响应出现;深度超过R/2的裂纹转子会出现分岔及混沌现象。裂纹角β对这些非线性动力学行为有很大影响。  相似文献   
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裂纹转子分叉、混沌行为研究中的映射延拓综合法   总被引:2,自引:2,他引:0  
介绍一种能全面计算周期激励下非线性系统周期响应,拟周期响应和混沌响应的新算法-映射延拓综合法,它可方便地确定拟周期响应和混沌响应对应的系统参数区间。应用此算法对具有非线性刚度的裂纹转子系统裂纹扩展故障特征问题进行了研究,得到了以裂纹深度为分叉参数的系统稳态响应分叉解图。  相似文献   
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徐培民  闻邦椿 《中国物理》2004,13(5):618-624
A simple branch of solution on a bifurcation diagram, which begins at static bifurcation and ends at boundary crisis (or interior crisis in a periodic window), is generally a period-doubling cascade. A domain of solution in parameter space, enclosed by curves of static bifurcation and that of boundary crisis (or the interior of a periodic window), is the trace of branches of solution. A P-n branch of solution refers to the one starting from a period-n (n≥1) solution, and the corresponding domain in parameter space is named the P-n domain of solution. Because of the co-existence of attractors, there may be several branches within one interval on a bifurcation diagram, and different domains of solution may overlap each other in some areas of the parameter space. A complex phenomenon, concerned both with the co-existence of attractors and the crises of chaotic attractors, was observed in the course of constructing domains of steady state solutions of the Hénon map in parameter space by numerical methods. A narrow domain of period-m solutions firstly co-exists with (lies on) a big period-n (m≥3n) domain. Then it enters the chaotic area of the big domain and becomes period-m windows. The co-existence of attractors disappears and is called the landing phenomenon. There is an interaction between the two domains in the course of landing: the chaotic area in the big domain is enlarged, and there is a crisis step near the landing area.  相似文献   
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