This paper has considered an automobile industry duopoly model with representative firms of kuaiche and taxi. The impact of product differentiation degree, market share of adaptive player and price adjustment speed of bounded rationality player on stability region and Nash equilibrium points of system have been analyzed. Numerical simulation has illustrated that product differentiation has increased the possibility of chaos, but chaos has existed not only in a fierce competitive market but also a weak competitive market. Another finding is that generally speaking, the increase of market share and product differentiation degree has increased equilibrium price of kuaiche and decreased equilibrium price of taxi. This means cash burning war strategy of kuaiche has worked. We choose different price adjustment speed to show dependence on initials only when the system is in chaos. We find suitable control factors to restrain and eliminate chaos.
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