An Effective Algorithm for the Stability and Bifurcation in a DDE Model of Gene Expression

The stability and Hopf bifurcation of gene expression models with a mechanism delayed state feedback are considered. An effective algorithm for the calculations on delay stable interval equilibrium point, direction, bifurcating periodic solution is also proposed. τ-decomposition strategy applied to tackle issue local stability, explicit formula provided. In addition, asymptotical behaviors solutions investigated by center manifold theorem normal form theory. direction determined naturally. subtle bilinear adjoint system proposed calculate parameters directly. Finally, correctness effectiveness our results verified typical numerical examples.