Abstract: In this paper,equations of dt/dXand dX/dt² of Logistic and Cui-Lawson models are calculated. When d²X/dt²=0,the increment turning point of Logistic equation can only lies at the point of K/2 and then maximum value of dX/dt is μ_L K/4; under the same condition,the increment turning point of Cui-Lawson equation lies at the point of K/(√b+1) and then the maximum value of dX/dt is μ_CK/(√b+1)². Through the variation of b,the Cui-Lawson equation may be superior than the Logistic when they are used to describe the law of population increment. By adopting the method of rotating coordinate with changing length of pace,comparisons between case fittings of these two equations are made. Logistic equation is also compared with Gause's,Andrewartha's,May's,Kreb's,Wan Changxiou's and Wang Mangmang's methods and results. Fitting results show that Cui-Lawson equation is the best and among the methods of fitting Logistic equation,the one described here is better.

Key words: Population increment, Theory comparison, Case fitting