Using a systematic computational approach and in vivo experiments, Cotterell et al.challenge a 40-year-old model that explains large-scale embryonic patterns in terms of long-range gradients.Instead, they show that these patterns can arise from short-range interactions and that a modified reaction diffusion mechanism can drive the self-organization observed during somitogenesis.In this paper, we inves-tigated the modified two dimensional model.It is suitable for exploring a design space of somitogenesis and can explain aspects of somitogenesis that previous models cannot.We mainly studied the non-diffusing case.We have used the Hopf bifurcation theorem,bifurcation theory and the Center manifold theorem in our investigation.Our model exhibits subcritical Hopf bifurcation for certain parameter values which marks the instability of limit cycles destroyed in Hopf bifurcations.And we get the condition in which the bistable state of the system exists.Because somitogenesis in the process of biological development occupies an important position,and as a pattern process can be used to study pattern formation and many aspects of embryogenesis.So our study have a great help for Embryonic development,gene expression,cell differen-tiation.In addition to,it is beneficial to study the clone animal variation problem of spinal bone number.