Almost sure exponential stability of stochastic reaction diffusion systems with Markovian jump}

The stochastic reaction diffusion systems may suffer sudden shocks‎, ‎in order to explain this phenomena‎, ‎we use Markovian jumps to model stochastic reaction diffusion systems‎. ‎In this paper‎, ‎we are interested in almost sure exponential stability of stochastic reaction diffusion systems with Markovian jumps‎. ‎Under some reasonable conditions‎, ‎we show that the trivial solution of stochastic reaction diffusion systems with Markovian jumps is almost surely exponentially stable‎. ‎An example is given to illustrate the theory‎. ‎