Control of a Multistable 3-ring Network of Chemical Oscillators

The Belousov-Zhabotinsky reaction is a limit cycle oscillator with dynamical attributes comparable to neurons. By fabricating microfluidic wells filled with the BZ chemistry, we create reaction-diffusion networks with rich dynamical patterns that can yield fundamental insights into dynamics of neural networks. A simple network of three inhibitor-coupled wells connected in a ring possesses two stable, dynamical steady states: clockwise and counterclockwise traveling waves. By photo-chemically perturbing the wells’ intrinsic frequencies we can force the system to switch states. In this work, we explore the steady states as a function of applied light gradient using the Kuramoto phase model and Vanaag-Epstein model for photosensitive BZ. Optimal control theory is then applied to determine the most efficient way to drive the system from one attractor to another.