Viktor Horvath, PhD
Postdoctoral Associate
Department of Chemistry
Brandeis University
(October 5, 2015)
Pulse-Coupled Chemical Oscillators: Experiments, Models, Theory
Like neurons, chemical reactions can oscillate. Depending on the concentrations, or strength, of the substances involved, the oscillations may display different behaviors. The behavior of chemical oscillators can give a unique look at the nature of a complex system, one that changes both with and in reaction to the substances it contains. Dr. Horvath described his work modeling the Belousov-Zhabotinsky oscillator. The model of oscillatory behavior he has developed is able to characterize how a pair of oscillators would function, based on the activity of one oscillator. This can have an impact on the modeling of oscillating neurons in the future.
Two identical pulse-coupled Belousov-Zhabotinsky (BZ) oscillators display various modes of synchronization as well as other interesting dynamical phenomena, like bursting and oscillatory death when their coupling strengths match. When the intrinsic frequencies of the two coupled oscillators initially match but the coupling strengths are unequal, this system may display a) phase locked oscillations, or b) stable temporal patterns where the frequencies of the oscillators no longer match (the peak alignments are fixed), or c) oscillator death. Similar behavior can be observed when the natural frequencies of the oscillators are significantly different and the coupling strengths are equal. Numerical simulations using a chemical model as well as in a phase model of the system show domains of various entrainment modes 1:1, 3:4, 2:3, 2:5, 1:2, 1:3, 1:4, etc., when the natural frequencies and/or the coupling strengths are varied. Here we demonstrate a method that enables us to find the combinations of the control parameters that produce a particular behavior. By using this method, we were able to characterize the collective behavior of a system of two BZ oscillators based on the dynamical features of a single pulse-perturbed BZ oscillator. This method is quite general and therefore it may be applicable to other systems where individual units that display oscillatory behavior are coupled via short pulses, such as networks of neurons.