International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 6, Pages 339-351
Moment Lyapunov exponent of delay differential equations
Nonlinear Manufacturing Systems Laboratory, Manufacturing Engineering Program, Worcester Polytechnic Institute, Worcester 01609-2280, MA, USA
Received 20 February 2001; Revised 9 September 2001
Copyright © 2002 M. S. Fofana. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The aim of this paper is to establish a connecting thread through
the probabilistic concepts of th-moment Lyapunov exponents, the integral averaging method, and Hale's reduction approach for delay dynamical systems. We demonstrate this connection by studying the stability of perturbed deterministic and stochastic differential equations with fixed time delays in the displacement and derivative functions. Conditions guaranteeing stable and unstable solution response are derived. It is felt that the connecting thread provides a unified framework for the stability study of delay differential equations in the deterministic and stochastic sense.