In this paper we have tried to stabilize the unstable fixed points for a class of 1-D maps by using a multiplicative nonlinear feedback control mechanism. We have also used such control to create new attractors (which did not exist in the original system), to suit our requirement. The control is also found to work in the presence of noise.

We demonstrate that chaos can be controlled using multiplicative exponential feedback control. Unstable fixed points, unstable limit cycles and unstable chaotic trajectories can all be stabilized using such control which is effective both for maps and flows. The control is of particular significance for systems with several degrees of freedom, as knowledge of only one variable on the desired unstable orbit is sufficient to settle the system onto that orbit. We find in all cases that the transient time is a decreasing function of the stiffness of control. But increasing the stiffness beyond an optimum value can increase the transient time. We have also used such a mechanism to control spatiotemporal chaos is a well-known coupled map lattice model.

We review the subject of control of chaotic systems paying special attention to exponential control. We also discuss the application of synchronization of chaotic systems to security in communications.