Control of chaotic solitons by time delay feedback

Piotr Fronczak and Janusz Holyst

We investigate a control of chaotic solitons using a modified time-delayed autosynchronization method. Numerical results for the maximal Lyapunov exponent are in very good agreement with analytical theory developed originally for low dimensional systems. The control is most efficient when the spatial distribution of the control force is proportional to the kink translational mode. Observations of the motion of the kink centre and the total power transmitted to the system lead to the same values of the maximal Lyapunov exponent.