ABSTRACT In a population model in continuous space, individuals evolve independently as branching random walks subject to immigration. If the underlying branching mechanism is subcritical, the model has a unique steady state for each value of the immigration intensity. Convergence to the equilibrium is exponentially fast. The resulting dynamics are Lyapunov stable in that their qualitative behavior does not change under suitable perturbations of the main parameters of the model.

中文翻译：

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连续空间中移民的人口模型

摘要 在连续空间中的人口模型中，个体作为分支随机游走独立进化，受到移民的影响。如果潜在的分支机制是次临界的，则该模型对于每个迁移强度值都有一个独特的稳态。收敛到均衡的速度呈指数级增长。由此产生的动力学是 Lyapunov 稳定的，因为它们的定性行为在模型主要参数的适当扰动下不会改变。