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In this paper, we study the dynamics of the ratio-dependent typeprey-predator model with different free boundaries. The two free boundaries,determined by prey and predator respectively, implying that they may intersecteach other as time evolves, are used to describe the spreading of prey andpredator. We mainly investigate the longtime behaviors of predator and prey.Then some sufficient conditions for spreading and vanishing are given. Inaddition, when spreading occurs, some estimates of asymptotic spreading speedsof u, v and asymptotic speeds of h, g are provided.

Dynamics for a Ratio-dependent Prey-predator Model with Different Free Boundaries