A note on the stationary distribution of the stochastic chemostat model with general response functions

Abstract A model of the chemostat involving stochastic perturbation is considered. Instead of assuming the familiar Monod kinetics for nutrient uptake, a general class of functions is used which includes both monotone and non-monotone uptake functions. Using the stochastic Lyapunov analysis method, under restrictions on the intensity of the noise, we show the existence of a stationary distribution and the ergodicity of the stochastic system.

[1]  Kai Liu.  Stochastic Stability of Differential Equations in Abstract Spaces , 2019 .

[2]  Gail S. K. Wolkowicz,et al.  Optimal biogas production in a model for anaerobic digestion , 2015 .

[3]  Sebastian Walcher,et al.  Exclusion and persistence in deterministic and stochastic chemostat models , 2005 .

[4]  Sanling Yuan,et al.  An analogue of break-even concentration in a simple stochastic chemostat model , 2015, Appl. Math. Lett..

[5]  Tonghua Zhang,et al.  Stability analysis of a chemostat model with maintenance energy , 2017, Appl. Math. Lett..

[6]  Gail S. K. Wolkowicz,et al.  Global dynamics of a mathematical model of competition in the chemostat: general response functions and differential death rates , 1992 .

[7]  Donal O'Regan,et al.  The periodic solutions of a stochastic chemostat model with periodic washout rate , 2016, Commun. Nonlinear Sci. Numer. Simul..

[8]  Fabien Campillo,et al.  Stochastic modeling of the chemostat , 2011 .

[9]  Sanling Yuan,et al.  Competition in the chemostat: A stochastic multi-species model and its asymptotic behavior. , 2016, Mathematical biosciences.

[10]  Gail S. K. Wolkowicz,et al.  A MATHEMATICAL MODEL OF THE CHEMOSTAT WITH A GENERAL CLASS OF FUNCTIONS DESCRIBING NUTRIENT UPTAKE , 1985 .

[11]  Gang George Yin,et al.  Asymptotic Properties of Hybrid Diffusion Systems , 2007, SIAM J. Control. Optim..

[12]  S. Zacks,et al.  Introduction to stochastic differential equations , 1988 .

[13]  Xinzhu Meng,et al.  Global dynamics analysis of a nonlinear impulsive stochastic chemostat system in a polluted environment , 2016 .

[14]  Audra E. Kosh,et al.  Linear Algebra and its Applications , 1992 .