Codimension-2 bifurcations of coupled BVP oscillators with hard characteristics

This manuscript is to study codimension-2 bifurcations for coupled nonlinear BVP oscillators with hard characteristics. Sufficient conditions are given for the model to demonstrate Hopf, Bogdanov–Takens (BT), double Hopf, and fold-Hopf bifurcations. By computing normal forms of those bifurcations, bifurcation diagrams such as Hopf, homoclinic, double limit cycle, and torus bifurcations are obtained. Some examples are given to confirm the theoretical results.

► We analyze coupled nonlinear BVP oscillators with hard characteristics.
► We give detailed conditions of parameters such that the oscillators have Hopf, BT, double Hopf, and zero-Hopf singularities.
► The normal forms of those singularities are computed and their corresponding bifurcation diagrams are obtained.
► Numerical simulations are given to verify the theoretical results.