Stability of minimum velocity wave

Although the previous discussion appears to permit any wave velocity from the spectrum in eqn (11.40), computed solutions and appropriate experimental evidence suggest that such systems adjust quickly so that they travel with the minimum speed allowed. This indicates that the wave with velocity cmin is somehow a stable solution, whereas those with higher speeds are unstable. 

The evaluation of stability for travelling-wave solutions is by no means a simple process and will not even be attempted here. The result that systems governed by quadratic Fisher equations tend to pick up their minimum permitted velocity will be used later. 

The reaction between iodate and arsenite ions appears to have contributions from both cubic and quadratic autocatalysis (the autocatalyst is the product, iodide ion). In the previous sections we have treated these two rate laws separately and by different methods. Both methods can be applied to the system in which these processes occur simultaneously, yielding results which, despite not being consistent at first sight, can be resolved by the idea of stability. 

If both reactions (11.1) and (11.30) occur, the dimensionless reaction-diffusion equation for the concentration of B in terms of the travelling-wave coordinate z can be written as 

Here he quantity q is a measure of the relative rates of the quadratic and cubic terms 

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