In this paper, a single reaction-diffusion population model with memory effect and the heterogeneity of the environment, equipped with the Neumann boundary, is considered. The global existence of a spatial nonhomogeneous steady state is proved by the method of super and subsolutions, which is linearly stable for relatively small memory-induced diffusion. However, after the memory-induced diffusion rate exceeding a critical value, spatial inhomogeneous periodic solution can be generated through Hopf bifurcation, if the integral of intrinsic growth rate over the domain is negative. Such phenomenon will never happen, if only memory-induced diffusion or spatially heterogeneity is presented, and therefore must be induced by their joint effects. This indicates that the memory-induced diffusion will bring about spatial-temporal patterns in the overall hostile environment. When the integral of intrinsic growth rate over the domain is positive, it turns out that the steady state is still linearly stable. Finally, the possible dynamics of the model is also discussed, if the boundary condition is replaced by Dirichlet condition.

在本文中，考虑了具有记忆效应和环境异质性的单一反应扩散种群模型，配备了诺依曼边界。空间非齐次稳态的全局存在通过超解和次解的方法证明，对于相对较小的记忆诱导扩散是线性稳定的。然而，在记忆诱导扩散率超过临界值后，如果域内固有增长率的积分为负，则可以通过 Hopf 分岔产生空间非均匀周期解。这种现象永远不会发生，如果只存在记忆诱导扩散或空间异质性，因此必须由它们的联合效应诱导。这表明记忆诱导的扩散将在整体敌对环境中带来时空模式。当域内内在增长率的积分为正时，表明稳态仍然是线性稳定的。最后，还讨论了模型的可能动力学，如果边界条件被狄利克雷条件代替。