Asymptotics of the solutions of the generalized Hutchinson equation. Automatic Control and Computer Sciences Volume 47, Issue 7, December 2013, Pages 470-494

The problem of the behavior of solutions of the Hutchinson equation and its generalizations is considered. Results regarding the estimation of the domain of the global stability of the positive equilibrium state in the parameter space are obtained. The problems of the existence, stability, and asymptotics of a slowly oscillating periodic solution are approached in the basic propositions. The problem of the dynamic properties of the system of ordinary differential equations that describes the well-known Belousov-Zhabotinsky reaction is considered as an application of the newly developed asymptotic methods.
Author keywords
Asymptotics; Differential equation with delay; Hutchinson equation; Large parameter; Periodic solution