Persistence in population models with demographic fluctuations (Q1085106)

In this paper the asymptotic behavior of a population is discussed which is governed by an equation of the form \(\dot x=xF(r(c(t)),x)\). The authors provide several sufficient conditions on F, r and c such that the solution x satisfies \[ \limsup_{t\to +\infty}x(t)>0,\quad or\quad \liminf_{t\to +\infty}x(t)>0\quad or\quad \liminf_{t\to +\infty}t^{-1}\int^{t}_{0}x(s)ds>0. \] It could, however, be mentionable that the original idea in investigating such equations with nonautomonous factors is due to Volterra by considering these as seasonal factors.