FKPP dynamics mediated by a parent field with a delay

In this poster we describe the result of modification of the Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) process in which the diffusing substance requires a parent density field for reproduction. This would be relevant in biological context, for example, with diffusing spores (propagules) and stationary fungus (parent). The parent produces propagules at a certain rate, and the propagules turn into the parent substance at another rate. A finite time is typically required for a new parent to mature before it begins to produce propagules. We model this evolution by a modified FKPP process with delay. Other types of delays in the FKPP model have been considered in the past as a mathematical construct. However, in our work, the delay arises in a natural science setting. The speed of the resulting density is shown to decrease with increasing delay time. Moreover, the front speed has a non-trivial dependence on the rate of conversion of propagules into new parent. The fronts in this model are always slower than Fisher waves of the classical FKPP model. The largest speed is half of the classical value - it is achieved at zero delay and when the two rates are matched.