Uniform persistence for population models with time delay using multiple Lyapunov functions (Q688885)

The authors consider dissipative population models with constant time lag \(a>0\) of the form \[ dx_ i/dt = x_ i f_ i(x(t-a)),\quad i=1,\ldots,n. \] Sufficient conditions for uniform persistence of positive solutions are given (i.e. conditions which ensure the existence of a \(d>0\) such that for any positive solution \(x\), \(\liminf x_ i(t)\geq d\) as \(t\to\infty\) for all \(i\)). The application of these conditions to several concrete models is discussed in detail.