Figure 3. A representative bistable system with diffusion shows the existence of non-homogenous solutions.

(A) Steady state solutions of the PDE (1) with f(z) = –α tan⁻¹(z), D = .1mm, and α = 2nM/min. Each solution corresponds to zero flux boundary conditions (i.e. u′(0) = u′(L) = 0) and varying state boundary conditions u(0) = –u(L). The equilibrium points of the bistable system are indicated by Ŧu^*. (B) Spatial profile corresponding to a half circle trip of the solution indicated in panel A with domain length L = 1.5mm. (C) Calculated domain length for each of the steady state solutions. The domain length approaches infinity as the boundary condition u(0) approaches Ŧu^*.