Dancing waves in reaction-diffusion systems

The mechanism of pattern formation in reaction- diffusion systems is treated as an interesting subject, generally for understanding self-organization observed in living systems and natural phenomena. Several spatial patterns appear in the reaction -diffusion systems where an activator and an inhibitor coexist as an intermediate, as represented by a traveling wave, a stationary wave called a Turing structure, etc. Here, we show new kinds of waves in reaction-diffusion systems, which exhibit reciprocating motion without colliding into each other or blinking periodically. These patterns have never been observed in the conventional numerical models, although experimentally oscillating spots have been often observed. Our model demonstrates that other than the ratio of diffusion coefficients for both intermediates, the thickness of reaction media acts to generate inhibitory effect. The spatial factor of the medium contributes to new pattern formation in reaction -diffusion systems. For the design of new functional materials, the concept might be useful as a simple controlling method for pattern dynamics.