Dynamical model of oscillatory zoning in plagioclase with nonlinear partition relation

We present a nonlinear dynamical model for oscillatory zoning in plagioclase based on a simple isothermal constitutive undercooling mechanism. A phenomenological partitioning is introduced to relate the concentration of An in the melt at the interface with the concentration in the solid. The non‐linearities in the model result from the coupling of the growth velocity with the local An concentration and from the boundary condition at the interface. The consideration of a nonlinear boundary condition is new and generalizes previous nonlinear growth models. It is shown that parameter values exist for which oscillatory solutions are possible via a Hopf bifurcation. As the system is driven further out of equilibrium, the model shows the development of chaotic solutions via a period‐doubling sequence.