Poster Presentation 2014 International Biophysics Congress

Two pulse-coupled non-identical, frequency-different BZ oscillators with time delay (#520)

Anastasia Lavrova 1 , Vladimir Vanag 1
  1. Immanuel Kant Baltic Federal University, Kaliningrad, Russia
The system of two identical pulse-coupled chemical oscillators has been investigated experimentally as well as theoretically [1]. This system has been presented by ferroin-catalyzed Belousov–Zhabotinsky (BZ) oscillators with time delay operated in continuously fed stirred tank reactors (CSTRs). To simulate experimental results, the five-variable model of the BZ reaction has been constructed [1].

 Herein, we study two non-identical chemical oscillators, using four-variable model of the Belousov-Zhabotinsky (BZ) reaction at mutual inhibitory, mutual excitatory, and mixed excitatory-inhibitory types of coupling[2].  The model has allowed us to analyze the effect of frequency difference on the resonant synchronization regimes of two-coupled oscillators and on the switching between these regimes. In particular, in comparing with previous results, we have performed a thorough phase analysis and identified parameters of time delay and coupling strengths that can efficiently induce switches in a system activity. It has been revealed that abrupt changes between different rhythms can occur depending on the coupling strengths and time delay between two oscillators, and there exist zones, where one of the oscillators is suppressed. We have shown that for weakly coupled oscillators (excitatory-inhibitory and mutual excitatory coupling), Farey sequence exists.
Such oscillators with time delay between a spike in one oscillator and a perturbation of the other one can be considered as the smallest basic element of neuronal networks coupled via synaptic connections [3]. Therefore results obtained in our work for various types of coupling may have an application in neuroscience.
  1. V. Horvath, P. Luigi Gentili, V. K. Vanag, and I. R. Epstein, Angew. Chem. Int. Ed., 51, 6878 (2012)
  2. Lavrova A. & V. Vanag, Phys. Chem. Chem. Phys., 16 (14), 6764 (2014)
  3. P. Goel and B. Ermentrout, Physica D, 2002, 163, 191.