Snapshots of three different realizations of the cyclic phase, revealing the microscopic dynamics behind the cycles of crime.

<p>Invasion fronts can be either led by the criminals (red), by the inspectors (green), or by ordinary individuals (blue). (<b>A–D</b>) For small inspection costs , large temptation and medium inspection incentives , the situation is initially dominated by inspectors, after which clusters of ordinary individuals spread. Then, a front of criminals invades the area of ordinary individuals, but they are chased by inspectors. As a result, inspectors prevail, with clusters of ordinary individuals and a few criminals in between. (<b>E–H</b>) For medium inspection costs , small temptation and medium inspection incentives , the situation is first dominated by ordinary individuals, then by criminals. Afterwards, inspectors form an invasion front entering the domain of criminals, followed by ordinary individuals. Eventually, the situation is dominated by ordinary individuals with some inspectors and criminal enclaves in between. (<b>I–L</b>) For even higher inspection costs , moderate temptation and medium inspection incentives , the evolutionary process is dominated by criminals in the early stage and later by inspectors. Finally, however, inspectors and criminals prevail, with a few clusters of ordinary individuals in between. Supplementary videos showing all three evolutionary processes from the beginning until the convergence to the stationary distribution of strategies are available at the following links: (<b>A–D</b>) youtube.com/watch?v = pH9l-2h6PRo, (<b>E–H</b>) youtube.com/watch?v = gVnCN3a9ki8, and (<b>I–L</b>) youtube.com/watch?v = ehlDSde3BM4.