In the weak radiation drive regime, the coupling between the thermal instability driven by impurity radiation and the self‐consistent flow profile modification leads to a simple dynamical system that can be approximated by the Volterra–Lotka equations. In this system the shear flow acts as a predator and the temperature fluctuations act as prey. The solutions are oscillatory, and their behavior resembles that of edge‐localized modes (ELM’s). The solutions of the simplified model are compared with the three‐dimensional and two‐dimensional nonlinear numerical results for this instability.