Asymptotics of Solutions of the Generalized Hutchinson’s Equation

Abstract

We discuss the dynamics of the Hutchinson’s equation and its generalizations. An estimate of the global stability region of a positive steady state is obtained. The main results refer to existence, stability and asymptotics of a slow oscillating solution. New asymptotic methods are applied to a problem of dynamical properties of ODE system describing Belousov — Zhabotinsky reaction.

Keywords

• delay differential equation
• hutchinson’s equation
• large parameter
• asymptotic
• periodic solution