Resonance and Pattern Formation in a Reaction Diffusion System

Bradley Marts

We can observe the phenomenon of resonance in any non-linear forced oscillator such as a pendulum. By confining an oscillatory chemical reaction to two dimensions, we create a field of non-linear oscillators. The oscillators are coupled by the diffusion of chemicals. The reaction is light sensitive and when forced with spatially homogenous light displays resonance features similar to that of a single oscillator[1]. An investigation of the 2:1 resonant tongue shows distinct spatial pattern formation[2]. These patterns are visually distinct and we investigate them mathematically by examining the distribution of the phases of the field of oscillators.

[1] V. Petrov, Q. Ouyang, and H.L. Swinney, Nature 388, 655 (1997)
[2] A. L. Lin, M. Bertram, K. Martinez, H. L. Swinney, A. Ardelea, and G. F. Carey, Phy. Rev. Lett. 84, 4240-4243

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