Bogdanov–Takens and triple zero bifurcations in general differential systems with m delays - Liu, Xia; Wang, Jingling (Nonlinear Analysis: Modelling and Control, 2016)
This paper mainly concerns the derivation of the normal forms of the Bogdanov–Takens (BT) and triple zero bifurcations for differential systems with m discrete delays. The feasible algorithms to determine the existence of the corresponding bifurcations of the system at the origin are given. By using center manifold reduction and normal form theory, the coefficient formulas of normal forms are derived and some examples are presented to illustrate our main results.