Randomly synchronizing chaotic systems
Journal
Progress of Theoretical Physics
Journal Volume
96
Journal Issue
4
Pages
683-692
Date Issued
1996
Author(s)
Abstract
Two identical nonlinear systems sometimes can be made to behave in a completely coherent yet chaotic way by continuously resetting some variable of one system using the corresponding variable of the other. The key to the success of this approach is that the exponential divergence typical of a chaotic attractor occurs in a direction which has a major component in the direction of the resetting variable, which is not always feasible. We show that this difficulty sometimes can be overcome by allowing the slave system to evolve freely for a certain time before reset is applied. It is further shown that the resets do not have to be applied at a regular time interval: a randomly selected sequence of reset times might be sufficient in bringing the two chaotic systems into complete synchronization. This added flexibility has the effect of broadening the power spectrum of the resetting variable, a fact which might find its potential applications in secure communications. A simple scaling relation for the lower bound of the admissible random reset time is also derived.
Type
journal article