Spatial periodicity induced by a chemical wave train

An all-chemical analog of clock-wave-front model for somitogenesis is proposed. The spatial periodicity can be obtained by arresting the homogeneous oscillations in a typical two-component reaction-diffusion system in the Hopf region by interacting with a chemical wave front. The patterns can be controlled by tuning the wave speed of the front.

Figure 1

Bifurcation diagram for CDIMA system exhibiting Hopf-Turing transition for $a=18.0$, $b=1.5$, and $d=1.6$.

Figure 2

Scheme of development of inhomogeneous spatial pattern.

Figure 3

Spatial [(a), (c), and (e)] and spatiotemporal [(b), (d), and (e)] evolution of concentrations while passing a wave train having speed of 0.003 [(a) and (b)], 0.0087 [(c) and (d)], and 0.0765 [(e) and (f)] unit or time, the parameters chosen are $a=18.0$ and $b=1.5$ in absence of wave train and $b=0$ in presence of wave, $d=1.6$, $\sigma =4.0$ (grid size $100\times 100$ with $\Delta x=\Delta y=1.0$ and $\Delta t=0.005$).

Figure 4

Variation in wavelength as a function of the velocity of the wave train with the parameter set $a=18.0$, $b=1.5$, $d=1.6$, and $\sigma =4.0$.

Figure 5

Variation in wavelength of spatial pattern as a function of the frequency of temporal oscillation with the parameter set $a=18.0$, $b=1.5$, $d=1.6$, and $\sigma =4.0$.