CONTROL OF CHAOS IN A DRIVEN NON LINEAR DYNAMICAL SYSTEM

We present a numerical study of a one-dimensional version of the Burridge-Knopoff model [16] of N-site chain of spring-blocks with stick-slip dynamics. Our numerical analysis and computer simulations lead to a set of different results corresponding to different boundary conditions. It is shown that we can convert a chaotic behaviour system to a highly ordered and periodic behaviour by making only small time-dependent perturbations. If part of the system (i.e., both ends) is wiggled by imposing the periodic force, then it is possible to approach the nearly stable solution even in a system which would otherwise be chaotic. The solutions are periodic in both time and space and display effects that are strikingly similar to those seen experimentally and numerically by Starrett and Tagg [6], Johnson et al. [7] and others. This case is very important in controlling chaos, reducing the noise in a noisy system and dynamical lubrication. We observe that for an arbitrary disordered set of initial conditions, the system can spontaneously organize itself so that the stable nearly periodic solutions emerge in a proper time. The average of power input is reduced in a sensitive way and a regular, stable, noise-free behaviour appears. The nature of the boundary conditions on the ends of the chain has a strong effect on the nature of the solutions and requires the parameters to be tuned in a proper way. We also study the possibility of taming spatiotemporal chaos with disorder and investigate the effect of broken symmetry in the system.