Stochastic stabilization and destabilization of nonlinear differential equations

This paper is concerned with the stochastic stabilization and destabilization of nonlinear differential equations, which, more precisely, further develops the general theory of stochastic stabilization and destabilization that was studied by Mao (1994) [4] and Appleby et al. (2008) [1]. The proposed results are of substantial improvements and reveal the more fundamental principle for stochastic stabilization and destabilization of dynamical systems, which is also verified with examples of application to mass-action systems.