Study of nonescape dynamics in Duffing oscillator with four different periodic forces

摘要

The effect of damping and the shape of four different periodic forces on nonescape dynamics in Duffing oscillator with double-hump potential is studied. Particularly, we numerically studied the variation of the amplitude f e of the external forces above which no attractor exists and the scaling of the size of basin of attraction of bounded motion with damping strength. We found $ f_{e} = beta ;e^{{alpha ,d,^{2} }} $ . The values of α and β are different for different periodic forces. The number of nonescaping initial conditions exhibit power-law variation $ N = beta ,(f_{e} - f)^{,alpha } $ . For each force different power-law relations are noticed above and below a value of the damping strength. The periodic forces of our interest are sine, modulus of sine, rectified sine and square-waves.