Pulse-coupled BZ oscillators with unequal coupling strengths

Abstract

Coupled chemical oscillators are usually studied with symmetric coupling, either between identical oscillators or between oscillators whose frequencies differ. Asymmetric connectivity is important in neuroscience, where synaptic strength inequality in neural networks commonly occurs. While the properties of the individual oscillators in some coupled chemical systems may be readily changed, enforcing inequality between the connection strengths in a reciprocal coupling is more challenging. We recently demonstrated a novel way of coupling chemical oscillators, which allows for manipulation of individual connection strengths. Here we study two identical, pulse-coupled Belousov-Zhabotinsky (BZ) oscillators with unequal connection strengths. When the pulse perturbations contain KBr (inhibitor), this system exhibits simple out-of-phase and complex oscillations, oscillatory-suppressed states as well as temporally periodic patterns (N : M) in which the two oscillators exhibit different numbers of peaks per cycle. The N : M patterns emerge due to the long-term effect of the inhibitory pulse-perturbations, a feature that has not been considered in earlier works. Time delay was previously shown to have a profound effect on the system's behaviour when pulse coupling was inhibitory and the coupling strengths were equal. When the coupling is asymmetric, however, delay produces no qualitative change in behaviour, though the 1 : 2 temporal pattern becomes more robust. Asymmetry in instantaneous excitatory coupling via AgNO3 injection produces a previously unseen temporal pattern (1 : N patterns starting with a double peak) with time delay and high [AgNO3]. Numerical simulations of the behaviour agree well with theoretical predictions in asymmetrical pulse-coupled systems.

Dynamical regimes of four almost identical chemical oscillators coupled via pulse inhibitory coupling with time delay

“…13 At present, the study of two pulse coupled BZ oscillators with a time delay is almost complete. [14][15][16][17] The BZ reaction is a catalyzed oxidation of malonic acid by bromate. 18,19 The time delay t between a spike in one oscillator (spike is a fast autocatalytic growth of the oxidized form of the catalyst and the activator, which is a HBrO 2 molecule) and the corresponding pulsatile perturbation of the other oscillator (which is a short pulse-injection of the inhibitor, Br À , in the case of inhibitory coupling or injection of AgNO 3 in the case of excitatory coupling) leads to unusual behavior such as in-phase synchronization for inhibitory coupling and fast anti-phase oscillations for excitatory coupling (at relatively large t).…”

In-materioneuromimetic devices: dynamics, information processing and pattern recognition

“…The dynamics of two pseudo-neurons has been investigated under both symmetrical inhibitory and/or excitatory coupling. 19,20 The latency caused by the propagation of action potentials has been emulated employing a delay between the appearance of a spike and the release of a pseudo-neurotransmitter. Both symmetrical and asymmetrical coupling can give rise to many temporal patterns.…”

New type of excitatory pulse coupling of chemical oscillators via inhibitor

“…To understand better the dynamics of pulse coupled oscillators with time delay, pulse coupling of chemical oscillators, such as the oscillatory Belousov-Zhabotinsky (BZ) reaction, 10,11 was introduced recently. [12][13][14][15] The BZ reaction is the metal-ion (or metallo-complex) catalysed oxidation of bromate by malonic acid in an acid medium.…”