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Global asymptotic stability of a ratio-dependent predator-prey system with diffusion. (English) Zbl 1093.35039

The authors investigate a predator-prey system with diffusion. The main attention is paid to the global asymptotic stability of the positive constant equilibrium of the system. In order to prove the main results, the authors consider the local asymptotic stability and then obtain some estimation of the solutions. The proof is completed by constructing Lyapunov functions, the method of upper and lower solutions combined with the monotone iteration.

MSC:

35K57 Reaction-diffusion equations
35B35 Stability in context of PDEs
92D25 Population dynamics (general)
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