Abstract: The change of demands in markets multi-companies that produce and sell similar products face and interaction among multi-companies will cause obvious non-linear relationship between supply and demand for similar products in the market. On the basis of unlinear catastrophe theory, the paper adopts geometric and gradient figures to well explain the catastrophic relationship between brand effects, product price and interactive factors among similar products which are caused by continuous change of multi-parameters and also points out measures companies should take in order to gain competitive advantage in the context of fierce competition.

Key words: productprice, hyperbolicumbilicicatastrophemodel, brandeffects