中文摘要：

研究有限格上的单种群生物模型，将种群的生活环境划分为有限斑块，每个斑块之间通过种群的扩散联系起来．通过对种群的出生函数和以种群的出生率和死亡率为元素的矩阵赋予一些假设来证明该系统的全局吸引子的存在性以及持久性．并且对于这样的一致持久系统，将进一步证明其存在一个内部吸引子并且在该内部吸引子内有一个共存态．

英文摘要：

The authors consider a lattice model for a single species in a one-dimensional patchy environment with finite number of patches connected by diffusion. Under some assumptions on birth functions and matrix component with death and diffusion rates, the authors showed the existence of global attractor and uniform persistence of the model by engaging persistence in infinite dimensional systems established by J. K. Hale and P. Waltman. Furthermore, for such a uniformly persistent system, the authors can prove that there exists an interior global attractor in which a coexistence steady state occurs.