Noise suppresses exponential growth for neutral stochastic differential delay equations

Our aim in this paper is to investigate the polynomial growth for a class of neutral stochastic differential delay systems. We reveal that environmental noise will suppress the exponential growth if it is sufficiently strong. That is, the given system (neutral ordinary differential delay equation) whose solution grows exponentially and becomes a new system (neutral stochastic differential delay equation) whose solution will grow polynomially with probability one. We also provide two examples to illustrate the main result.