Irregular wakes in reaction-diffusion waves

Reaction-diffusion equations have proved to be highly successful models for a wide range of biological and chemical systems, but chaotic solutions have been very rarely documented. We present a new mechanism for generating apparently chaotic spatiotemporal irregularity in such systems, by analysing in detail the bifurcation structure of a particular set of reaction-diffusion equations on an infinite one-dimensional domain, with particular initial conditions. We show that possible solutions include travelling fronts which leave behind either regular or irregular spatiotemporal oscillations. Using a combination of analytical and numerical analysis, we show that the irregular behaviour arises from the instability of oscillations induced by the passage of the front. Finally, we discuss the generality of this mechanism as a way in which spatiotemporal irregularities can arise naturally in reaction-diffusion systems.