Geometric methods of global attraction in systems of delay differential equations
06-03-2018 06:41
In this paper we deduce criteria of global attraction in systems of delay differential
equations. Our methodology is new and consists in “dominating” the nonlinear terms of the
system by a scalar function and then studying some dynamical properties of that function.
One of the crucial benefits of our approach is that we obtain delay-dependent results of
global attraction that cover the best delay-independent conditions. We apply our results in a
gene regulatory model and the classical Nicholson's blowfly equation with patch structure.