Inhibitory and excitatory pulse coupling of two frequency-different chemical oscillators with time delay

Abstract

Dynamical regimes of two pulse coupled non-identical Belousov-Zhabotinsky oscillators have been studied experimentally as well as theoretically with the aid of ordinary differential equations and phase response curves both for pure inhibitory and pure excitatory coupling. Time delay τ between a spike in one oscillator and perturbing pulse in the other oscillator plays a significant role for the phase relations of synchronous regimes of the 1:1 and 1:2 resonances. Birhythmicity between anti-phase and in-phase oscillations for inhibitory pulse coupling as well as between 1:2 and 1:1 resonances for excitatory pulse coupling have also been found. Depending on the ratio of native periods of oscillations T2/T1, coupling strength, and time delay τ, such resonances as 1:1 (with different phase locking), 2:3, 1:2, 2:5, 1:3, 1:4, as well as complex oscillations and oscillatory death are observed.

Emergence and combinatorial accumulation of jittering regimes in spiking oscillators with delayed feedback

“…However, there is a very easy criterion reflecting this structure, which is the presence of regions with slope < -1 in the PRC. PRCs possessing this property have been experimentally measured here for the electronic oscillator and by other authors for chemical oscillators [71,72] and cardiac cells [73][74][75]. As for neurons, PRCs with steep falling parts have been observed [59], but there is no data whether their slope can be less than -1 or not.…”

Phase response curves for models of earthquake fault dynamics

“…the point that the effect of perturbation depends on the dynamical state of the oscillator. In its representation as a phase oscillator, each oscillator possesses a characteristic P RC that can be computed numerically or measured experimentally [64][65][66][67][68] .…”

Introduction to Focus Issue: Oscillations and Dynamic Instabilities in Chemical Systems: Dedicated to Irving R. Epstein on occasion of his 70th birthday

“…44 These techniques were greatly refined, for example, to demonstrate the role of inhibitory and excitatory pulse coupling of chemical oscillators. 45 The group of Vladimir Vanag 46 reports that the dynamical regimes of two pulse-coupled non-identical BZ oscillators with delay can exhibit amplitude death and higher-order entrainments depending on the coupling strength and time delay. Irv Epstein demonstrated birhythmicity (two different modes of oscillations under the same conditions) in chlorite-bromate-iodide system with Mohammed Alamgir.…”