Stochastic suppression and stabilization of functional differential equations

Abstract: Without the linear growth condition or the one-sided linear growth condition, this paper discusses whether or not stochastic noise feedback can stabilize a given unstable nonlinear functional system . Since may defy the linear growth condition or the one-sided linear growth condition, this system may explode in a finite time. To stabilize this system, this paper stochastically perturbs this system into the stochastic functional differential system by two independent Brownian motions and . This paper shows that the Brownian motion may suppress the potential explosion of the solution for appropriate . Moreover, for sufficiently large , this stochastic functional system is exponentially stable. These results can be used to examine stochastic stabilization. [ABSTRACT FROM AUTHOR]