Boundary-induced pattern formation from temporal oscillation: Spatial map analysis

Takahiro Kohsokabe, Kunihiko Kaneko
2016 Europhysics letters  
Boundary-induced pattern formation from a spatially uniform state is investigated using one-dimensional reaction-diffusion equations. The temporal oscillation is successively transformed into a spatially periodic pattern, triggered by diffusion from the fixed boundary. We introduced a spatial map, whose temporal sequence, under selection criteria from multiple stationary solutions, can completely reproduce the emergent pattern, by replacing the time with space. The relationship of the pattern
more » ... ip of the pattern wavelength with the period of oscillation is also obtained. The generality of the pattern selection process and algorithm is discussed with possible relevance to biological morphogenesis.
doi:10.1209/0295-5075/116/48005 fatcat:chbdjuupured3ka72dymf5rpce