Figure 1

Computer simulation of the paths \(\pmb{S(t)}\) , \(\pmb{x_{1}(t)}\) , \(\pmb{x_{2}(t)}\) , \(\pmb{c(t)}\) for the deterministic chemostat model ( 1 ) and the stochastic chemostat model ( 2 ) with parameters \(\pmb{S_{0}=4}\) , \(\pmb{Q=0.5}\) , \(\pmb{r_{1}=0.5}\) , \(\pmb{r_{2}=0.9}\) , \(\pmb{\delta_{1}=2}\) , \(\pmb{\delta _{2}=2.2}\) , \(\pmb{a_{1}=15}\) , \(\pmb{a_{2}=7.5}\) , \(\pmb{\mu_{1}=2.7}\) , \(\pmb{\mu_{2}=1.4}\) , \(\pmb{h=0.5}\) , \(\pmb{u=0.3}\) , \(\pmb{\tau =10}\) and the initial values \(\pmb{S(0)=2.5}\) , \(\pmb{x_{1}(0)=1}\) , \(\pmb{x_{2}(0)=1}\) , \(\pmb{c(0)=0.3}\) . (a) Time series for \(S(t)\), \(X_{1}(t)\), \(X_{2}(t)\), \(c(t)\) with parameters \(\sigma_{1}=0\), \(\sigma_{2}=0\). (b) Time series for \(S(t)\), \(X_{1}(t)\), \(X_{2}(t)\), \(c(t)\) with parameters \(\sigma_{1}=2.4\), \(\sigma_{2}=1.2\). (c) Time series for \(S(t)\), \(X_{1}(t)\), \(X_{2}(t)\), \(c(t)\) with parameters \(\sigma_{1}=0.2\), \(\sigma_{2}=1.2\). (d) Time series for \(S(t)\), \(X_{1}(t)\), \(X_{2}(t)\), \(c(t)\) with parameters \(\sigma_{1}=2.4\), \(\sigma_{2}=0.1\). (e) Time series for \(S(t)\), \(X_{1}(t)\), \(X_{2}(t)\), \(c(t)\) with parameters \(\sigma_{1}=0.2\), \(\sigma_{2}=0.1\).