关键词: 灰色Verhulst模型, GM（1, 1）幂模型, 粒子群算法

Abstract: Based on the grey Verhulst model，in this paper the equidistance and non-equidistance GM（1，1） power model is studied.The models’ solutions are got.The relations of the model’s curve and power’s exponent，development coefficient are analyzed.The average relative error is seen as a function of power’s exponent，development coefficient and grey action quantity.At the same time the initial condition is considered.The Particle Swarm Optimization（PSO） algorithm is used to solve the models’ parameters.Then the defects of the grey Verhulst model and the least square method are overcome.Finally one example shows the precision of the GM（1，1） power model with parameter identification based on PSO is higher than the grey Verhulst model.So the method is feasible，effective and has important theory significance.

Key words: grey Verhulst model, GM（1, 1） power model, Particle Swarm Optimization（PSO）