Control of Complex Dynamics with Time-Delayed Feedback in Populations of Chemical Oscillators: Desynchronization and Clustering

Abstract

Control of collective dynamics with global time-delayed feedback was experimentally studied with (phase) synchronized populations of smooth, relaxational, and chaotic electrochemical oscillators. The experimental results provide laboratory evidence for the findings in the studies of delayed feedback on phase oscillators; multiple, isolated regions of desynchronization in the parameter plane, hysteresis phenomenon around the boundaries of control regions, synchronization of irregular behavior with very strong feedback strength, and a shift of the synchronization transition curves were reproduced in experiments. In addition, it is observed that clustering accompanies the occurrence of desynchronization in delayed feedback of relaxational oscillators. For populations of elements that are close to Hopf bifurcation, desynchronization, amplitude death, and enhanced synchronization occurs with a low, intermediate, and high delay time, respectively.