| Predator-prey models describe the interaction among species,they are impor-tant models in the population dynamics,which can apply to many scientific fields comprehensively.The paper studies a class of fast-slow predator-prey models with the prey growing much faster than the predator,that is,the growth rate of the prey is fast,while the growth rate of the predator is slow.By using basic calculus analysis and phase plane analysis,we first obtain the effect of the fast growth rate of prey on the asymptotic behavior of limit cycle of planar systems,and the limit cycle exhibits the temporal patterns of a stable relaxation oscillator.Using the basic tools of partial differential and linearization analysis,we further obtain the influence of the rapid growth of the prey on the boundness and stability of solutions of the reaction-diffusion system. |
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