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An understanding of the underlying mechanism of side--branching is paramountin controlling and/or therapeutically treating mammalian organs, such as lungs,kidneys, and glands. Motivated by an activator-inhibitor-substrate approachthat is conjectured to dominate the initiation of side--branching in pulmonaryvascular pattern, I demonstrate a distinct transverse front instability inwhich new fingers grow out of an oscillatory breakup dynamics at the frontline, without any typical length scale. These two features are attributed tounstable peak solutions in 1D that subcritically emanate from the Turingbifurcation and that exhibit repulsive interactions. The results are based on abifurcation analysis and numerical simulations, and provide a potentialstrategy toward developing a framework of side--branching also of otherbiological systems, such as plant roots and cellular protrusions.

The nonlinear initiation of side--branching by activator-inhibitor-substrate (Turing) morphogenesis