Boundary Conditions Cause Different Generic Bifurcation Structures In Turing Systems

The study revisited Turing's theory of morphogenesis, focusing on how boundary conditions affect bifurcation structures in Turing systems. It was found that while Turing bifurcations typically occur through a pitchfork bifurcation under zero-flux boundary conditions, they become transcritical under fixed boundary conditions. This conclusion was derived using weakly nonlinear analysis and applied to Schnakenberg kinetics. The research highlighted the importance of considering variations in boundary conditions, not just parameter perturbations, in sensitivity analyses of specific applications.