Abstract
The ergodicity of solutions for stochastic systems has been widely concerned by many scholars in recent years. Thus, in this paper, we further analyze the geometric ergodicity of a stochastic chemostat model with general nutrient uptake function. By verifying minorization condition and Lyapunov condition, geometric ergodicity of stochastic chemostat system is presented, which means the transfer probability of Markov process will converge to its limiting distribution at an exponentially rate. Meanwhile, we prove that the solution of stochastic system is stochastically ultimately bounded.
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