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.

A hierarchical network of pulse coupled chemical micro-oscillators and excitable cells demonstrates intelligent behavior.

Switching between stable oscillatory modes in a network of four Belousov–Zhabotinsky oscillators unidirectionally coupled in a ring analysed computationally and experimentally.

We introduce a new type of pulse coupling between chemical oscillators. A constant inflow of inhibitor in one reactor is interrupted shortly after a time delay after a sharp spike of activity in the other reactor. We proved experimentally and theoretically that this reversed inhibitory coupling is analogous to excitatory coupling. We did this by analyzing phase response curves, dependences of different synchronous regimes of the 1 : 1 resonance on time delay, and other resonances of two coupled chemical oscillators. Dynamical rhythms of two Belousov-Zhabotinsky oscillators coupled via "negative" inhibitory pulses were investigated.

We present an experimental system of four identical microreactors (MRs) in which the photosensitive oscillatory Belousov‐Zhabotinsky (BZ) reaction occurs. The inhibitory coupling of these BZ MRs is organized via pulses of light coming to each MR from a computer projector. These pulses are induced by spike(s) in other MR(s) of the same network. Time delay between the spike in one BZ MR and the pulsed perturbation of the other BZ MR(s), the amplitude of light pulses, their duration, and the connectivity of the MRs are controlled by the LabVIEW software. Recording the dynamics of the BZ reaction in the MRs via a microscope equipped with a CCD camera, we observe all the main dynamical modes of our network of MRs, which are the IP (in‐phase), AP (anti‐phase), W (walk), and WR (walk reverse) for the unidirectional coupling, and the IP, two‐cluster, three‐cluster, and splay modes for the all‐to‐all coupling. Our software detects all the modes of the network automatically and makes it possible to switch between them on demand using a few special “switching” pulses. As the result of the present work, the experimental implementation of the adaptive behaviour of the pulse‐coupled chemical micro‐oscillator networks becomes available.

We have investigated the effect of global negative feedback (GNF) on the dynamics of a 1D array of water microdroplets (MDs) filled with the reagents of the photosensitive oscillatory Belousov-Zhabotinsky (BZ) reaction. GNF is established by homogeneous illumination of the 1D array with the light intensity proportional to the number of BZ droplets in the oxidized state with the coefficient of proportionality ge. MDs are immersed in the continuous oil phase and diffusively coupled with the neighboring droplets via inhibitor Br2 which is soluble in the oil phase. At chosen concentrations of the BZ reactants, illumination suppresses the BZ oscillators. Without GNF, or at a very small ge < 0.29, local inhibitory coupling leads to out-of-phase oscillations of the neighboring BZ droplets with an almost constant phase shift Δφ between them, which makes a space-time plot of the BZ MDs look like a staircase. At 0.3 < ge < 0.6, regular oscillatory clusters consisting of distant BZ MDs (mostly 5-6 phase clusters) emerge. At 0.6 ≤ ge ≤ 1.0, chaotic clusters are observed. At 1.2 < ge < 1.8, regular (mostly 3-4-phase) clusters emerge again. At 1.8 < ge < (3-4), complex clusters with different (but multiple) periods of oscillation are observed. At the same time, some droplets stop oscillating. At large enough ge (>4), in the region of two-phase clusters (with several suppressed BZ MDs), final patterns seem to resemble the initial patterns. Intensive computer simulations with the ordinary differential equations support experimental results.

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