基于粒子群算法的带群混沌吸引子参数的生成

Generation of Chaotic Attractor Parameter Vectors with Frieze Groups Based on PSO

文中以带群等价映射模型p1a1为例,详细论述了模型p1a1混沌吸引子的构造方法与过程。将粒子群算法(PSO)应用于搜索具有平面带群对称性混沌吸引子的参数问题,构造了参数向量作为粒子的表达方法,建立了此问题的粒子群算法。试验结果表明,粒子群算法可以快速、有效求得各参数向量的最优解,并且有效地避免了优生遗传算法的"遗传漂移"问题,是优化参数向量的一个较好方案,从而解决了在巨大参数空间下生成具有平面带群对称性混沌吸引子困难的问题。

Taking the model of pl al-equivarient mappings of frieze groups for example, discuss in detail the model＇s structure methods and processes. Introduce a proposal to extend the heuristic called ＂ particle swarm optimization＂ （PSO） to deal with the problem of searching chaotic parameters of chaotic attractors with planar frieze symmetries in the multi-parameter space, and propose a novel particle presentation for the chaotic parameter vectors. Experimental results indicate that the PSO can effectively and quickly get optimal resolution of the chaotic parameter vectors and avoid the ＂genetic drift＂ phenomenon from the eugenic genetic algorithm effectively,so it is proved to be an effective method for the optimization of parameter vector, solving the problem of generating chaotic attractors with planar frieze symmetries in large parameter space difficultly.