Effects of calcium input/output on the stability of a system for calcium-regulated viscoelastic strain fields.

The Goodwin and Trainor model of pattern generation in calcium-regulated strain fields is studied in the case where calcium input and calcium output processes are involved. It is shown that the properties of the original model may still remain provided that the input-output processes are not unstable. In this last case, despite the eventual stabilizing effect of the calcium exchange term, perturbations of the generalized system can grow and lead to inhomogeneous solutions. Applications to cell differentiation and cell growth are discussed.