Stationary peaks in a multivariable reaction–diffusion system: foliated snaking due to subcritical Turing instability

An activator-inhibitor-substrate model of side-branching used in the context pulmonary vascular and lung development is considered on supposition that spatially localized concentrations activator trigger local side-branching. The consists four coupled reaction-diffusion equations its steady solutions therefore obey an eight-dimensional spatial dynamical system one dimension (1D). Stationary structures within are found to be associated with a subcritical Turing instability organized distinct type foliated snaking bifurcation structure. This behavior turn presence exchange point parameter space at which complex leading eigenvalues uniform concentration state overtaken by pair real eigenvalues; this plays role Belyakov-Devaney system. primary structure periodic spike or peak trains $N$ identical equidistant peaks, $N=1,2,\dots \,$, together cross-links consisting nonidentical, nonequidistant peaks. complicated multitude multipulse states, some also computed, spans range from all way fold $N=1$ state. These states form template physical develop transverse direction 2D.