Stability and boundedness criteria for certain second-order nonlinear neutral stochastic functional differential equations.

Ademola, A. T.; Wen, S.; Feng, Y.; Zhang, W.; Rutkowski, L.

This paper presents stochastic stability and stochastic boundedness for certain second-order nonlinear neutral stochastic differential equations. The second-order differential equation is transformed into a neutral stochastic system of first-order equations and combined with a second-order quadratic function to derive a Lyapunov-Krasovskiĭ functional. This functional is then utilized to establish criteria on the nonlinear functions to ensure novel results on stochastic stability and stochastic asymptotic stability of the zero solution. Furthermore, when the forcing term is nonzero, new results on stochastic boundedness and uniform stochastic boundedness of solutions are derived. The results presented in this paper are original and improve upon existing literature. Two special cases of the theoretical results are provided to illustrate the practical application of the findings.

STOCHASTIC differential equations; NONLINEAR differential equations; DIFFERENTIAL equations; STOCHASTIC systems; STABILITY criterion

Proyecciones - Journal of Mathematics, 2024, Vol 43, Issue 5, p985

0716-0917

Academic Journal

10.22199/issn.0717-6279-6146