Resonant pattern formation in a chemical system

A periodic force applied to a nonlinear pendulum can cause the pendulum to become entrained at a frequency that is rationally related to the applied frequency, a phenomenon known as frequency-locking(1). A recent theoretical analysis showed that an array of coupled nonlinear oscillators can exhibit spatial reorganization when subjected to external periodic forcing(2). We present here experimental evidence that reaction-diffusion processes, which govern pattern evolution and selection in many chemical and biological systems(3), can also exhibit frequency-locking phenomena. For example, periodic optical forcing of the light-sensitive Belousov-Zhabotinsky (BZ) reaction transforms a rotating spiral wave(4) to a labyrinthine standing-wave pattern (Fig. 1). As the forcing frequency is varied, we observe a sequence of frequency-locked regimes, analogous to the frequency-locked 'tongues' of a driven nonlinear pendulum, except that in the reactor different frequencies correspond to different spatial patterns. Resonant interactions leading to standing-wave patterns have not been observed previously in chemical or biological media, but periodic forcing (such as circadian rhythm) is abundant in nature and may lead to similar pattern-forming phenomena.