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中文摘要：
建立了带扩散的具有Holling Ⅲ类功能性反应的捕食模型，讨论了模型的一致持久性，应用特征子空间分解与线性化的方法得到了模型正平衡点局部稳定性的充分条件，进一步通过构造适当的Lyapunov泛函的方法得到了正平衡点全局稳定性的充分条件．
英文摘要：
A Holling type Ⅲ predator-prey with diffusion system subject to the homogeneous Neumann boundary condition was studied. Results show that the system is uniformly persistent under some appropriate conditions. The sufficient condition of local asymptotic stability of the system positive equilibrium was obtained by applying the characteristic subspace decomposition and linearization method. Further, the sufficient condition of global asymptotic stability of the system positive equilibrium was obtained by establishing a suitable Lyapunov functionelle.
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