Destruction of dissipative structures under random actions

We consider random-parameter chemical kinetic systems that are important in numerous physical, chemical, and biological applications. Random parameters describe the action of ambient medium fluctuations on the system. We estimate the probability that the system state remains in a given domain of the phase space during a time interval $[0,T]$ under the condition that the state at the initial instant was in $u_0$, where $u_0$ is the equilibrium solution describing a dissipative structure. We show that in some cases, the problem of maximizing this probability is reducible to the known problem of minimizing the Hopfield Hamiltonian.