Bifurcation and transitional dynamics in asymmetrical two-coupled oscillators with hard type nonlinearity

The paper investigates various global bifurcations and related changes of dynamics, including the transitional phenomenon, in asymmetrical two-coupled oscillators with hard type nonlinearity. There exist periodic attractors for comparatively large ε (a parameter showing the degree of nonlinearity), and they disappear for small ε via saddle-node bifurcation. We draw nodes and saddles with their unstable manifold near the bifurcation point on the Poincare section for various values of k² (deviation between two oscillators´ intrinsic frequencies). It is recognized that the unstable manifold changes a lot with parameter variation around the bifurcation point, and hence the associated dynamics change drastically.