“…For instance, addition of constant bias [4][5][6], quadratic nonlinear term x 2 [4,[7][8][9], variable shape parametric perturbation [10,11], replacing cubic nonlinearity by the quadratic nonlinear term [12][13][14] and asymmetrical periodic driving force [15] have physical significance and represent real physical systems in different disciplines. In the presence of such symmetry breaking perturbations, the occurrence of homoclinic bifurcation, structure of strange attractors, hysteresis jump, routes to chaos, basin boundary structure and escape dynamics have been investigated in the Duffing oscillator.…”