Multi-condition of stability for nonlinear stochastic non-autonomous delay differential equation
A nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for exponential mean square stability of the linear part of the considered...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
VTeX
2018-08-01
|
| Series: | Modern Stochastics: Theory and Applications |
| Subjects: | |
| Online Access: | https://www.vmsta.org/journal/VMSTA/article/128/text |
| _version_ | 1819205705294413824 |
|---|---|
| author | Leonid Shaikhet |
| author_facet | Leonid Shaikhet |
| author_sort | Leonid Shaikhet |
| collection | DOAJ |
| description | A nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for exponential mean square stability of the linear part of the considered nonlinear equation also are sufficient conditions for stability in probability of the initial nonlinear equation. Some new sufficient condition of stability in probability for the zero solution of the considered nonlinear non-autonomous stochastic differential equation is obtained which can be considered as a multi-condition of stability because it allows to get for one considered equation at once several different complementary of each other sufficient stability conditions. The obtained results are illustrated with numerical simulations and figures. |
| first_indexed | 2024-12-23T04:55:57Z |
| format | Article |
| id | doaj.art-ad7a3168072d45798140fca52521c2c5 |
| institution | Directory Open Access Journal |
| issn | 2351-6046 2351-6054 |
| language | English |
| last_indexed | 2024-12-23T04:55:57Z |
| publishDate | 2018-08-01 |
| publisher | VTeX |
| record_format | Article |
| series | Modern Stochastics: Theory and Applications |
| spelling | doaj.art-ad7a3168072d45798140fca52521c2c52022-12-21T17:59:22ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542018-08-015333735110.15559/18-VMSTA110Multi-condition of stability for nonlinear stochastic non-autonomous delay differential equationLeonid Shaikhet0Tel-Aviv UniversityA nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for exponential mean square stability of the linear part of the considered nonlinear equation also are sufficient conditions for stability in probability of the initial nonlinear equation. Some new sufficient condition of stability in probability for the zero solution of the considered nonlinear non-autonomous stochastic differential equation is obtained which can be considered as a multi-condition of stability because it allows to get for one considered equation at once several different complementary of each other sufficient stability conditions. The obtained results are illustrated with numerical simulations and figures.https://www.vmsta.org/journal/VMSTA/article/128/textNonlinear stochastic differential equationorder of nonlinearity higher than onevarying coefficientsdiscrete and distributed delaysexponential mean square stabilitystability in probabilityregions of stability |
| spellingShingle | Leonid Shaikhet Multi-condition of stability for nonlinear stochastic non-autonomous delay differential equation Modern Stochastics: Theory and Applications Nonlinear stochastic differential equation order of nonlinearity higher than one varying coefficients discrete and distributed delays exponential mean square stability stability in probability regions of stability |
| title | Multi-condition of stability for nonlinear stochastic non-autonomous delay differential equation |
| title_full | Multi-condition of stability for nonlinear stochastic non-autonomous delay differential equation |
| title_fullStr | Multi-condition of stability for nonlinear stochastic non-autonomous delay differential equation |
| title_full_unstemmed | Multi-condition of stability for nonlinear stochastic non-autonomous delay differential equation |
| title_short | Multi-condition of stability for nonlinear stochastic non-autonomous delay differential equation |
| title_sort | multi condition of stability for nonlinear stochastic non autonomous delay differential equation |
| topic | Nonlinear stochastic differential equation order of nonlinearity higher than one varying coefficients discrete and distributed delays exponential mean square stability stability in probability regions of stability |
| url | https://www.vmsta.org/journal/VMSTA/article/128/text |
| work_keys_str_mv | AT leonidshaikhet multiconditionofstabilityfornonlinearstochasticnonautonomousdelaydifferentialequation |