Dynamics of a stochastic turbidostat model with sampled and delayed measurements

Abstract

In this paper, a stochastic turbidostat model with controllable output is established by using piecewise constant delayed measurements of the substrate concentration. We commence by proving the existence and uniqueness of the global positive solution of the stochastic delayed model. Then, sufficient conditions of extinction and stochastic strong permanence of the biomass are acquired. In quick succession, we investigate the stochastic asymptotical stability of the washout equilibrium as well as the asymptotic behavior of the random paths approaching the interior equilibrium of its corresponding deterministic model by employing the method of Lyapunov functionals. Numerical and theoretical findings show that the influence of environmental random fluctuations on the dynamics of the model may be more pronounced than that of time delay.

Keywords

• turbidostat
• delay
• feedback control
• strongly stochastically permanent
• asymptotic behavior