Title: Waves and Chaos in Oscillatory Systems

Artworks submitted by: Jonathan Sherratt and Matthew Smith

Many natural populations undergo multi-year cycles, and field studies have shown that these can be organized into periodic travelling waves. Mathematical studies have shown that large-scale landscape obstacles represent a natural mechanism for wave generation. This figure show a numerical simulation of this process of wave generation for a caricature model of an oscillatory ecological system. In the left hand panel the obstacle is the small central circle, and it generates a stable wave pattern. But in the right hand panel the obstacle is larger, and this causes the generation of a wave that is of lower amplitude and is unstable. It is visible close to the obstacle but then breaks down into spatiotemporal chaos. In oscillatory systems, invasion generates a spatiotemporal transition through periodic cycles,leading ultimately to spatiotemporal chaos.