Bifurcation analysis of the generalized stretch-twist-fold flow

Based on the stretch-twist-fold flow, a generalized stretch-twist-fold flow is introduced. By choosing an appropriate bifurcation parameter, Hopf bifurcations occur in this system when the bifurcation parameter exceeds a critical value. The formulae for determining the direction of the Hopf bifurcations and the stability of bifurcating periodic solutions are presented. In addition, the paper also investigates the bifurcations of the heteroclinic orbits for this system. The existence and its associated existing regions are given for two heteroclinic orbits, respectively. Finally, some numerical simulations for justifying the theoretical analysis are presented.