Emergent Synchronous Volumetric Oscillation in Hierarchically Structured Self-Oscillating Gel Clusters

Emergent properties accompanying synchronization among oscillators are vital characteristics in biological systems. Belousov-Zhabotinsky (BZ) oscillators are an artificial model to study the emergence and synchronization in life. This research represents a self-oscillating gel system with clusterable properties to experimentally examine synchronous and emergent properties at a fundamental hierarchical level. Incorporating acrylic acid (AAc) moieties within the gel network facilitates cluster formation through hydrogen bonding in an acidic BZ substrate solution. Upon clustering, both homogeneous and heterogeneous gel assemblies─ranging from double to quadruple clusters─exhibit increased and synchronized periods and amplitudes during the BZ reaction. Notably, in heterogeneous clusters, gel units with initially short periods and small volumetric amplitudes display a significant increase, aligning with the lonfger periods and larger amplitudes of other elements within the cluster, an emergent property. This research can pave the way for a better understanding of synchronous and emergent properties in biological oscillators such as cardiomyocytes.

A programmable hybrid digital chemical information processor based on the Belousov-Zhabotinsky reaction

The exponential growth of the power of modern digital computers is based upon the miniaturization of vast nanoscale arrays of electronic switches, but this will be eventually constrained by fabrication limits and power dissipation. Chemical processes have the potential to scale beyond these limits by performing computations through chemical reactions, yet the lack of well-defined programmability limits their scalability and performance. Here, we present a hybrid digitally programmable chemical array as a probabilistic computational machine that uses chemical oscillators using Belousov-Zhabotinsky reaction partitioned in interconnected cells as a computational substrate. This hybrid architecture performs efficient computation by distributing information between chemical and digital domains together with inbuilt error correction logic. The efficiency is gained by combining digital logic with probabilistic chemical logic based on nearest neighbour interactions and hysteresis effects. We demonstrated the computational capabilities of our hybrid processor by implementing one- and two-dimensional Chemical Cellular Automata demonstrating emergent dynamics of life-like entities called Chemits. Additionally, we demonstrate hybrid probabilistic logic as a viable logic for solving combinatorial optimization problems.

Chemical micro-oscillators based on the Belousov–Zhabotinsky reaction

The results of studies on the development of micro-oscillators (MOs) based on the Belousov –Zhabotinsky (BZ) oscillatory chemical reaction are integrated and systematized. The mechanisms of the BZ reaction and the methods of immobilization of the catalyst of the BZ reaction in micro-volumes are briefly discussed. Methods for creating BZ MOs based on water microdroplets in the oil phase and organic and inorganic polymer microspheres are considered. Methods of control and management of the dynamics of BZ MO networks are described, including methods of MO synchronization. The prospects for the design of neural networks of MOs with intelligent-like behaviour are outlined. Such networks present a new area of nonlinear chemistry, including, in particular, the creation of a chemical ‘computer’.

The bibliography includes 250 references.

Dynamics of Reaction-Diffusion Oscillators in Star and other Networks with Cyclic Symmetries Exhibiting Multiple Clusters

We experimentally and theoretically investigate the dynamics of inhibitory coupled self-driven oscillators on a star network in which a single central hub node is connected to k peripheral arm nodes. The system consists of water-in-oil Belousov-Zhabotinsky ∼100  μm emulsion drops contained in storage wells etched in silicon wafers. We observed three dynamical attractors by varying the number of arms in the star graph and the coupling strength: (i) unlocked, uncorrelated phase shifts between all oscillators; (ii) locked, arm hubs synchronized in phase with a k-dependent phase shift between the arm and central hub; and (iii) center silent, a central hub stopped oscillating and the arm hubs oscillated without synchrony. We compare experiment to theory. For case (ii), we identified a logarithmic dependence of the phase shift on star degree, and were able to discriminate between contributions to the phase shift arising from star topology and oscillator chemistry.

"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_inh of the perturbing pulses. At C_inh > C_cr, a new pseudo-steady state (SS) emerges far away from the limit cycle of the unperturbed BZ oscillator. The perturbed BZ system spends rather long time in the vicinity of this pseudo-SS, which serves as a trap for phase trajectories. As a result, the dynamics of the BZ system changes qualitatively. We observe new modes with packed spikes separated by either long "silent" dynamics or small-amplitude oscillations around pseudo-SS, depending on C_inh. Networks of two or three LV-BZ oscillators with strong pulsatile coupling and self-inhibition are able to generate so-called "cognitive" modes, which are very sensitive to small changes in C_inh. We demonstrate how the coupling between the BZ oscillators in these networks should be organized to find "cognitive" modes.

Phase-frequency model of strongly pulse-coupled Belousov-Zhabotinsky oscillators

We demonstrate that the dynamical behavior of strongly pulse-coupled Belousov-Zhabotinsky oscillators can be reproduced and predicted using a model that treats both the phase and the instantaneous frequency of the oscillators. Model parameters are extracted from the experimental data obtained using a single pulse-perturbed oscillator and are used to simulate the temporal dynamics of a system of two coupled oscillators. Our model exhibits the out-of-phase and anti-phase synchronization and the 1:N and N:M temporal patterns as well as the oscillator suppression that are observed in experiments when the inhibitory coupling is asymmetric. This approach may be adapted to other systems, such as coupled neurons, where the oscillatory dynamics is affected by strong pulses.

Autonomous cycling between excitatory and inhibitory coupling in photosensitive chemical oscillators

Photochemically coupled Belousov-Zhabotinsky micro-oscillators are studied in experiments and simulations. The photosensitive oscillators exhibit excitatory or inhibitory coupling depending on the surrounding reaction mixture composition, which can be systematically varied. In-phase or out-of-phase synchronization is observed with predominantly excitatory or inhibitory coupling, respectively, and complex frequency cycling between excitatory and inhibitory coupling is found between these extremes. The dynamical behavior is characterized in terms of the corresponding phase response curves, and a map representation of the dynamics is presented.

Pulse-coupled Belousov-Zhabotinsky oscillators with frequency modulation

Inhibitory perturbations to the ferroin-catalyzed Belousov-Zhabotinsky (BZ) chemical oscillator operated in a continuously fed stirred tank reactor cause long term changes to the limit cycle: the lengths of the cycles subsequent to the perturbation are longer than that of the unperturbed cycle, and the unperturbed limit cycle is recovered only after several cycles. The frequency of the BZ reaction strongly depends on the acid concentration of the medium. By adding strong acid or base to the perturbing solutions, the magnitude and the direction of the frequency changes concomitant to excitatory or inhibitory perturbations can be controlled independently of the coupling strength. The dynamics of two BZ oscillators coupled through perturbations carrying a coupling agent (activator or inhibitor) and a frequency modulator (strong acid or base) was explored using a numerical model of the system. Here, we report new complex temporal patterns: higher order, partially synchronized modes that develop when inhibitory coupling is combined with positive frequency modulation (FM), and complex bursting patterns when excitatory coupling is combined with negative FM. The role of time delay between the peak and perturbation (the analog of synaptic delays in networks of neurons) has also been studied. The complex patterns found under inhibitory coupling and positive FM vanish when the delay is significant, whereas a sufficiently long time delay is required for the complex temporal dynamics to occur when coupling is excitatory and FM is negative.

Dynamical regimes of four oscillators with excitatory pulse coupling

Dynamics of four almost identical chemical oscillators pulse coupled via excitatory coupling with time delays are systematically studied.

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

The dynamics of four almost identical pulse coupled chemical oscillators with time delay are systematically studied.

New type of excitatory pulse coupling of chemical oscillators via inhibitor

A new type of excitatory pulse coupling of two chemical oscillators via a short interruption of inhibitor inflow is introduced.