强迫Vanderpol振子的吸引子和吸引域特征

Character of Attractors and Domains of Attraction in Forced Van der pol Oscillator

利用点映射 胞映射综合法对强迫Vanderpol振子的周期吸引子和吸引域进行数值分析 ,模拟了吸引子的内部结构 ,除了发现在复杂过渡区有多吸引子共存外 ,还发现奇数周期吸引子和偶数周期吸引子具有不同的拓扑结构· 奇数周期吸引子为中心对称形吸引子 ,偶数周期吸引子互为中心对称·将分析域划分成 82 77、10 197、12 5 35、15 0 0 0、10 432 5和 40 0 5 45个胞 ,分别计算它们的吸引域时 ,发现周期吸引子的吸引域具有分数维的性质· 点映射

Attractors and the domains of attraction in forced Van der pol oscillator were studied by means of point mapping cell mapping syntheses method. The structure of attractors were simulated by numerical method. The odd attractors and even attractors have different structures except that the multiple attractors coexist in complex successive domains. The odd attractors possess the shape of center symmetry and even attractors take the shape of centre symmetry each other. The domains of attraction were calculated respectively when there are 8277、10197、12535、15000、104325 and 400545 cells in the analyses domains. The domains of attraction have fractional dimension. Point mapping cell mapping syntheses method is of high accuracy and efficiency.