Effects of Random Excitations on the Dynamical Response of Duffing Systems

We study the dynamics of a Duffing oscillator excited by correlated random perturbations for both fixed and periodically modulated stiffness. In the case of fixed stiffness we see that Poincare map gets distorted due to the random excitation and, the distortion increases with the increase of correlation of the field. In a strongly correlated field, however, the map becomes purely random. We analyse the maximum value of the Lyapunov exponent and see that the random response competes with the chaotic motion to increase the stability of the system. In the case of periodically modulated stiffness, the periodic parametric excitation causes the Duffing system to execute dynamics of two fixed-point attractors. These attractors remain non-chaotic even in the presence of random field but can get merged due to induced fluctuation in the trajectory. It is seen that the random field can change the status of the system from transit to stable state.

Automated summary

In the case of fixed stiffness, strong correlated random excitations distort the Poincare map, making it purely random, while random response competes with chaotic motion to enhance system stability. In the case of periodically modulated stiffness, random fields can change the system's state from transient to stable.