Ayman M. Mahmoud, Abd Elmotaleb A. M. A. Elamin, Shiraz E. A. Elhussein and Mawadda E.  Eboelhasan
Some Qualitative Properties of Solutions For Multi-Delay Nonautonomous Stochastic Lienard Equation
Dynamic Systems and Applications 32 (2023)  81-101

https://doi.org/10.46719/dsa2023.32.06

ABSTRACT.
In this study, we analyse the nonautonomous multi-delay stochastic Lienard equation and develop sucient conditions for the equation’s stability and boundedness. The Lyapunov functional (LF) technique is used as the primary instrument in the proofs and we extend and enhance some stability and boundedness conclusions from the literature through our work. Two examples are used to support the correctness and ecacy of the results as an application. Finally, using the Euler-Maruyama method (EM-method), numerical simulations are provided in the nal part to illustrate the approximative numerical solutions for the Lienard system under consideration.

AMS (MOS) Subject Classication. 34C11, 34K20, 34K50, 60H35.

Key Words and Phrases. Multi-delay, Stochastic Lienard equation, Stability, Boundedness, Lyapunov functional approach, EM-method.