$$\frac{d L}{dt } = \kappa (L_f-L)$$ (22)

where $\kappa = 0.04$ and $L_{f} = 3$.

Figure: Plot of $L(t)$ and $E(0,t)$ starting from constant initial data $E(x,0) = 0.0$, $A(x,0)=0.0$, $L(0) = 0.01$. The parameter values are $K_A = 1.0$,$V_A = 1.0$,$A_0 = 0.05$, $\delta = 0.1$, $k_A = 0.2$,$k_E = 0.1$, $\rho=0.3$, $\alpha = 1.0$, and $L=2.0$.

Figure: Plot of $L(t)$ and $E(0,t)$ starting from constant initial data $E(x,0) = 0.0$, A$(x,0) = 0.0$, $L(0) = 0.01$. The parameter values are $K_A = 1.0$, $V_A = 1.0$, $A_0 = 0.05$, $\delta = 0.1$, $k_A = 0.2$, $k_E = 0.1$, $\rho=0.3$, $\alpha = 1.0$, and $L=2.0$.

To see a movie demonstrating the bistability of this system click here.