Cascading Bifurcations

Sequential bifurcation of solutions of nonlinear equations, as the bifurcation parameter increases, is called cascading bifurcation. It has been proposed as a mechanism to describe the transition from laminar to turbulent fluid flows, and as a mechanism for chemical and biochemical morphogenesis and pattern formation. The creation of cascading bifurcation by the splitting of multiple primary bifurcation points is described. A perturbation method is employed in the analysis. Primary, secondary, tertiary, etc. bifurcation points and states are determined for a specific nonlinear boundary value problem.