Moment Lyapunov exponent of delay differential equations
The aim of this paper is to establish a connecting thread through the probabilistic concepts of pth-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 determin...
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Hindawi Limited
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202012103 |
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doaj-e9620ca8efdb475e91764bccd1752d6c2020-11-24T21:22:59ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0130633935110.1155/S0161171202012103Moment Lyapunov exponent of delay differential equationsM. S. Fofana0Nonlinear Manufacturing Systems Laboratory, Manufacturing Engineering Program, Worcester Polytechnic Institute, Worcester 01609-2280, MA, USAThe aim of this paper is to establish a connecting thread through the probabilistic concepts of pth-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.http://dx.doi.org/10.1155/S0161171202012103 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
M. S. Fofana |
| spellingShingle |
M. S. Fofana Moment Lyapunov exponent of delay differential equations International Journal of Mathematics and Mathematical Sciences |
| author_facet |
M. S. Fofana |
| author_sort |
M. S. Fofana |
| title |
Moment Lyapunov exponent of delay differential equations |
| title_short |
Moment Lyapunov exponent of delay differential equations |
| title_full |
Moment Lyapunov exponent of delay differential equations |
| title_fullStr |
Moment Lyapunov exponent of delay differential equations |
| title_full_unstemmed |
Moment Lyapunov exponent of delay differential equations |
| title_sort |
moment lyapunov exponent of delay differential equations |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2002-01-01 |
| description |
The aim of this paper is to establish a connecting thread through
the probabilistic concepts of pth-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. |
| url |
http://dx.doi.org/10.1155/S0161171202012103 |
| work_keys_str_mv |
AT msfofana momentlyapunovexponentofdelaydifferentialequations |
| _version_ |
1725994057581199360 |