Random impacts of a complex damped system

We investigated the random impacts of a complex damped system. Firstly the interested deterministic complex damped system was revisited and the unstable periodic attractors could be found by means of Poincaré map, time evolution and phase plot since the top Lyapunov exponent could not be applied to decide the unstable states of the proposed system. Secondly the stochastic complex damped system was examined and random impacts would be discovered, namely, the initial deterministic system will be stabilized using the stochastic force properly. The top Lyapunov exponent versus the noise intensity will be observed and one can find the change of dynamical behaviors from instability to stability. Also we implemented Poincaré map analysis, time history and phase plot to confirm the obtained results of top Lyapunov exponent, and we can find excellent agreement between these results. Therefore random noise can be applied to control the dynamical behaviors.