Oscillations and travelling waves

Abstract

A very important class of shell patterning is caused by pigment productions that occur only during a short time interval, followed by an inactive period without pigment production. Stripes parallel to the growing edge and oblique lines belong to this class of patterns. Oscillations can occur if the antagonist reacts too slowly. A change in activator concentration cannot be immediately regulated again causing activation to proceed in a burst-like manner. Only after a sufficient accumulation of the inhibitor, or after a severe depletion of the substrate, will activator production collapse. A refractory period will follow with very low activator production in which either the excess inhibitor will degrade or the substrate will accumulate until a new activation becomes possible. The condition for oscillatory activations is the reverse of that given for stable patterns. In an activator-inhibitor scheme, oscillations occur if the decay rate of the inhibitor is smaller than that of the activator i.e., if the condition r _b < r _a in Equation 2.1 (page 23) is satisfied.