Tianran Chen

Date of Graduation


Document Type


Degree Type



Eberly College of Arts and Sciences



Committee Chair

Kenneth Showalter

Committee Co-Chair

Fabien Goulay

Committee Member

Justin Legleiter

Committee Member

Mark Tinsley


The emergence of collective behavior has been observed in all levels of biological systems, for example, the aggregation of slime mold, swarm motion of insects and the collective motion in schools of sh. Synchronization is one of the most important collective behaviors and can play a pivotal role in maintaining the normal function of a living system, such as pacemaker cells in the heart, circadian rhythms, and insulin release from pancreatic cells. Synchronization typically arises as a result of the interaction of large ensembles of oscillators. Studies of the Belousov-Zhabotinsky (BZ) chemical oscillators have shown a variety of collective dynamical behaviors, such as phase clusters, dynamical quorum sensing and chimera states. The discovery of echo phenomena in large populations of coupled Kuramoto oscillators motivates us to study this dynamical behavior using photosensitive BZ oscillators.;In this thesis, we examine echo behavior experimentally and mathematically. The experiments are carried out with a BZ micro-oscillator system. A large system of micro-oscillators is achieved by the design of a large oscillator array (LOA), which permits coupling of over 1000 oscillators. The dimensionless Zhabotinsky, Buchholtz, Kiyatkin and Epstein (ZBKE) mathematical model is used to investigate the behavior. The experiment and numerical results illustrate that if a BZ system of oscillators is subject to two perturbations, separated by time tau, then at the time tau after second perturbation, the oscillators show a measurable response in their collective signal. Factors such as noise and size of the perturbation impacting the magnitude of the echo are examined and a theoretical calculation of the magnitude of the echo as a function of the size of the perturbation exhibits good agreement with simulation results using the ZBKE model.