In this talk I will describe some properties of Meinhardt's model of sidebranching. This is a four-species reaction-diffusion model dating from 1976 describing the interaction of four fields, the concentrations of an activator, an inhibitor, the substrate, and a marker for differentiation. The model exhibits rich dynamics that are absent from simpler RD systems. I will describe two of these: propagation failure of differentiation fronts and, in a different parameter regime, the presence of intermittent spiking. The former is traced to the presence of so-called T-points in parameter space. The latter is characterized by a Poisson probability distribution function of interspike intervals, indicating that the spiking process is memoryless. The role of a (subcritical) Turing instability in generating (unstable) spikes will be emphasized.

This is joint work with Arik Yochelis, Ben-Gurion University, Be'er Sheva, Israel.