Stabilization and destabilization of nonlinear stochastic differential delay equations

ABSTRACT

This present paper deals with the problem of stabilization and destabilization of nonlinear stochastic differential delay equations. The key techniques used in this paper are the LaSalle-type stability theorems, the nonnegative semimartingale convergence theorem, and the law of large numbers for martingales. The proposed results can be applied to study the stabilization and destabilization of more general nonlinear stochastic dynamical time-delay systems. Computer simulations are presented to illustrate our theory.

KEYWORDS:

• Stochastic differential delay equations
• LaSalle-type stability theorems
• Nonnegative semimartingale convergence theorem
• Stochastic stabilization
• Stochastic destabilization

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China (61673103) and the Fundamental Research Funds for the Central Universities and Graduate Student Innovation Fund of Donghua University (CUSF-DH-D-2019086).