Implementation of Hebb's rules in a network of excitable chemical cells coupled by pulses.

A network of four excitable cells with the Belousov-Zhabotinsky (BZ) reaction is considered both theoretically and experimentally. All cells are coupled by pulses with time delays between the moment of a spike in cell # and the moment of the corresponding perturbation of an addressee (cell #). The coupling strengths of all connections except the coupling strength between cells #1 and #2 are constant.

Plasticity in networks of active chemical cells with pulse coupling.

A method for controlling the coupling strength is proposed for pulsed coupled active chemical micro-cells. The method is consistent with Hebb's rules. The effect of various system parameters on this "spike-timing-dependent plasticity" is studied.

Oscillatory microcells connected on a ring by chemical waves.

The dynamics of four coupled microcells with the oscillatory Belousov-Zhabotinsky (BZ) reaction in them is analyzed with the aid of partial differential equations. Identical BZ microcells are coupled in a circle via identical narrow channels containing all the components of the BZ reaction, which is in the stationary excitable state in the channels. Spikes in the BZ microcells generate unidirectional chemical waves in the channels.

Distance dependent types of coupling of chemical micro-oscillators immersed in a water-in-oil microemulsion.

A system of micro-spheres immersed in a water-in-oil microemulsion (ME) is studied both theoretically and experimentally. A catalyst for the Belousov-Zhabotinsky (BZ) reaction is immobilized in the micro-spheres, which are called BZ micro-oscillators (BZ MOs). The ME is loaded with all the reagents of the BZ reaction, except the catalyst.

Experimental verification of an opto-chemical "neurocomputer".

A theoretically predicted hierarchical network of pulse coupled chemical micro-oscillators and excitable micro-cells that we call a chemical "neurocomputer" (CN) or even a chemical "brain" is tested experimentally using the Belousov-Zhabotinsky reaction. The CN consists of five functional units: (1) a central pattern generator (CPG), (2) an antenna, (3) a reader for the CPG, (4) a reader for the antenna unit, and (5) a decision making (DM) unit. A hybrid CN, in which such chemical units as readers and DM units are replaced by electronic units, is tested as well.

Size- and position-dependent bifurcations of chemical microoscillators in confined geometries.

The present theoretical study deals with microparticles (beads) that contain an immobilized Belousov-Zhabotinsky (BZ) reaction catalyst. In the theoretical experiment, a BZ bead is immersed in a small water droplet that contains all of the BZ reaction reagents but no catalyst. Such heterogeneous reaction-diffusion BZ systems with the same BZ reactant concentrations demonstrate various dynamic modes, including steady state and low-amplitude, high-amplitude, and mixed-mode oscillations (MMOs).

Fabrication of New Belousov-Zhabotinsky Micro-Oscillators on the Basis of Silica Gel Beads.

We have fabricated and examined silica gel beads loaded with a catalyst of the Belousov-Zhabotinsky (BZ) reaction, tris(2,2'-bipyridyl)ruthenium(II) chloride, Ru(bpy)Cl, the BZ beads. The abilities of silica gel and the widely used ion-exchange resin (Dowex 50WX2) BZ beads to oscillate in a catalyst-free BZ solution are compared. The period of the BZ oscillations increases with an increase in the diameter (40-250 μm) of both types of the BZ beads.

Hierarchical network of pulse coupled chemical oscillators with adaptive behavior: Chemical neurocomputer.

We consider theoretically a network of pulse coupled oscillators with time delays. Each oscillator is described by the Oregonator-like model for the Belousov-Zhabotinsky (BZ) reaction. Different groups of oscillators constitute five functional units: (1) a central pattern generator (CPG), (2) a "reader" unit that can identify dynamical modes of the CPG, (3) an antenna (A) unit that receives external signals and responds on them by generating different dynamical modes, (4) another reader unit for identification of the dynamical modes in the A unit, and (5) a decision making unit that switches the current dynamical mode of the CPG to the mode that is similar to the current mode in the A unit.

Experimental Investigation of the Dynamical Modes of Four Pulse-Coupled Chemical Micro-Oscillators.

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.

"Cognitive" modes in small networks of almost identical chemical oscillators with pulsatile inhibitory coupling.

The Lavrova-Vanag (LV) model of the periodical Belousov-Zhabotinsky (BZ) reaction has been investigated at pulsed self-perturbations, when a sharp spike of the BZ reaction induces a short inhibitory pulse that perturbs the BZ reaction after some time τ since each spike. The dynamics of this BZ system is strongly dependent on the amplitude C of the perturbing pulses. At C > C, a new pseudo-steady state (SS) emerges far away from the limit cycle of the unperturbed BZ oscillator.

Controllable switching between stable modes in a small network of pulse-coupled chemical oscillators.

Switching between stable oscillatory modes in a network of four Belousov-Zhabotinsky oscillators coupled in a ring via unidirectional inhibitory pulsatile coupling with a time delay is analysed computationally and experimentally. There are five stable modes in this network: in-phase, anti-phase, walk, walk reverse, and three-cluster modes. Transitions between the modes are carried out by short external pulses applied to one or several oscillators.

Dynamics of a 1D array of inhibitory coupled chemical oscillators in microdroplets with global negative feedback.

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.

Dynamical modes of two almost identical chemical oscillators connected via both pulsatile and diffusive coupling.

The dynamical regimes of two almost identical Belousov-Zhabotinsky oscillators with both pulsatile (with time delay) and diffusive coupling have been studied theoretically with the aid of ordinary differential equations for four combinations of these types of coupling: inhibitory diffusive and inhibitory pulsatile (IDIP); excitatory diffusive and inhibitory pulsatile; inhibitory diffusive and excitatory pulsatile; and finally, excitatory diffusive and excitatory pulsatile (EDEP). The combination of two types of coupling creates a condition for new feedback, which promotes new dynamical modes for the IDIP and EDEP coupling.

Dynamic modes in a network of five oscillators with inhibitory all-to-all pulse coupling.

The dynamic modes of five almost identical oscillators with pulsatile inhibitory coupling with time delay have been studied theoretically. The models of the Belousov-Zhabotinsky reaction and phase oscillators with all-to-all coupling have been considered. In the parametric plane C-τ, where C is the coupling strength and τ is the time delay between a spike in one oscillator and pulsed perturbations of all other oscillators, three main regimes have been found: regular modes, when each oscillator gives only one spike during the global period T, C (complex) modes, when the number of pulses of different oscillators is different, and OS (oscillations-suppression) modes, when at least one oscillator is suppressed.

A 'reader' unit of the chemical computer.

We suggest the main principals and functional units of the parallel chemical computer, namely, (i) a generator (which is a network of coupled oscillators) of oscillatory dynamic modes, (ii) a unit which is able to recognize these modes (a 'reader') and (iii) a decision-making unit, which analyses the current mode, compares it with the external signal and sends a command to the mode generator to switch it to the other dynamical regime. Three main methods of the functioning of the reader unit are suggested and tested computationally: (a) the polychronization method, which explores the differences between the phases of the generator oscillators; (b) the amplitude method which detects clusters of the generator and (c) the resonance method which is based on the resonances between the frequencies of the generator modes and the internal frequencies of the damped oscillations of the reader cells. Pro and contra of these methods have been analysed.

Dynamical regimes of four oscillators with excitatory pulse coupling.

The dynamical regimes of four almost identical oscillators with pulsatile excitatory coupling have been studied theoretically with two models: a kinetic model of the Belousov-Zhabotinsky reaction and a phase-reduced model. Unidirectional coupling on a ring and all-to-all coupling have been considered. The time delay τ between the moments of a spike in one oscillator and a pulse perturbation of the other(s) plays a crucial role in the emergence of the dynamical modes, which are classified as regular, complex, and OS (oscillation-suppression)-modes.

Self-Organization Induced by Self-Assembly in Microheterogeneous Reaction-Diffusion System.

When acrylamide (AA) monomers are added to the Belousov-Zhabotinsky (BZ) reaction incorporated into nanodroplets of water-in-oil aerosol OT (AOT) microemulsion (the BZ-AOT system), free radicals produced in the BZ reaction initiate polymerization of AA monomers and polyacrylamide particles are formed. These particles change the microstructure of the AOT microemulsion thus inducing the transition from Turing patterns to new dissipative patterns which can be either stationary "black" spots or waves.

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

The dynamic regimes in networks of four almost identical spike oscillators with pulsatile coupling via inhibitor are systematically studied. We used two models to describe individual oscillators: a phase-oscillator model and a model for the Belousov-Zhabotinsky reaction. A time delay τ between a spike in one oscillator and the spike-induced inhibitory perturbation of other oscillators is introduced.

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

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.

New type of excitatory pulse coupling of chemical oscillators via inhibitor.

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.

Two pulse-coupled non-identical, frequency-different BZ oscillators with time delay.

Two non-identical, frequency-different pulse-coupled oscillators with time delay have been systematically studied using four-variable model of the Belousov-Zhabotinsky (BZ) reaction at mutual inhibitory, mutual excitatory, and mixed excitatory-inhibitory types of coupling. Different resonances like 1 : 2, 2 : 3, 1 : 3, etc., as well as complex rhythms and abrupt changes between them occur depending on the coupling strengths, time delay, and frequency ratio.

Effect of solvents on the pattern formation in a Belousov-Zhabotinsky reaction embedded into a microemulsion.

Using the ferroin- and the bathoferroin-catalyzed Belousov-Zhabotinsky (BZ) reaction embedded in the sodium-bis (2-ethylhexyl) sulfosuccinate (AOT) water-in-oil microemulsion, we observed different patterns occurring in two different solvents, hexane and octane. Turing patterns were found in both solvents with ferroin. They differ in their interaction with coexisting bulk oscillations, such that a new excitation front was formed around the evolving Turing patterns in hexane.

Two- and three-dimensional standing waves in a reaction-diffusion system.

We observe standing waves of chemical concentration in thin layers [quasi-two-dimensional (2D)] and capillaries [three-dimensional (3D)] containing the aqueous Belousov-Zhabotinsky reaction in a reverse microemulsion stabilized by the ionic surfactant sodium bis-2-ethylhexyl sulfosuccinate (AOT) and with cyclo-octane as the continuous phase. The 3D structures are oscillatory lamellae or square-packed cylinders at high and low volume fractions, respectively, of aqueous droplets. These patterns correspond to oscillatory labyrinthine stripes and square-packed spots in the 2D configuration.

Pulse-coupled chemical oscillators with time delay.

Finger on the pulse: in a system of two pulse-coupled Belousov-Zhabotinsky oscillators, introducing a time delay or increasing the coupling strength brings about novel dynamic features (see picture, the two oscillators are shown in different colors), such as reversal of the roles of excitatory and inhibitory coupling or fast anti-phase oscillation. These features are not observed in diffusively coupled systems, and shed light on how such pulse coupling occurs at synapses.

Excitatory and inhibitory coupling in a one-dimensional array of Belousov-Zhabotinsky micro-oscillators: theory.

We study numerically the behavior of one-dimensional arrays of aqueous droplets containing the oscillatory Belousov-Zhabotinsky reaction. Droplets are separated by an oil phase that allows coupling between neighboring droplets via two species: an inhibitor, Br(2), and an activator, HBrO(2). Excitatory coupling alone (through the activator) generates in-phase oscillations and/or "waves," while inhibitory coupling alone (through Br(2)) gives rise to antiphase oscillations, Turing patterns, and their combinations.