Bifurcation analysis of a System Modelling Somite Formation

Abstract This paper deals with stability and bifurcation analysis of a minimal models of vertebrae formation. Conditions are derived under which there can be no change in stability. Using one of the parameters as a bifurcation parameter it is found that various type of bifurcations occurs when the parameter passes through a critical value. Applying the centre manifold theory and the normal form method formulas are given for describing the qualitative properties of the current bifurcation. Computer simulations illustrate the results. Mathematics Subject Classifications: 92B05 (34D20, 34C23, 34K20).