Title: Permanency of the age-structured population model on several temporally variable patches,
Abstract: We consider a system of nonlinear partial differential equations that
describes an age-structured population inhabiting several temporally varying
patches. We prove existence and uniqueness of solution and analyze its
large-time behavior in cases when the environment is constant and when it
changes periodically. A pivotal assumption is that individuals can disperse and
that each patch can be reached from every other patch, directly or through
several intermediary patches. We introduce the net reproductive operator and
characteristic equations for time-independent and periodical models and prove
that permanency is defined by the net reproductive rate for the whole system.
If the net reproductive rate is less or equal to one, extinction on all patches
is imminent. Otherwise, permanency on all patches is guaranteed. The proof is
based on a new approach to analysis of large-time stability.