Phase Clusters in Large Populations of Chemical Oscillators

Mixtures Recomposition by Neural Nets: A Multidisciplinary Overview

Artificial Neural Networks (ANNs) are transforming how we understand chemical mixtures, providing an expressive view of the chemical space and multiscale processes. Their hybridization with physical knowledge can bridge the gap between predictivity and understanding of the underlying processes. This overview explores recent progress in ANNs, particularly their potential in the 'recomposition' of chemical mixtures. Graph-based representations reveal patterns among mixture components, and deep learning models excel in capturing complexity and symmetries when compared to traditional Quantitative Structure-Property Relationship models. Key components, such as Hamiltonian networks and convolution operations, play a central role in representing multiscale mixtures. The integration of ANNs with Chemical Reaction Networks and Physics-Informed Neural Networks for inverse chemical kinetic problems is also examined. The combination of sensors with ANNs shows promise in optical and biomimetic applications. A common ground is identified in the context of statistical physics, where ANN-based methods iteratively adapt their models by blending their initial states with training data. The concept of mixture recomposition unveils a reciprocal inspiration between ANNs and reactive mixtures, highlighting learning behaviors influenced by the training environment.

A Goodwin Model Modification and Its Interactions in Complex Networks

The global economy cannot be understood without the interaction of smaller-scale economies. We addressed this issue by considering a simplified economic model that still preserves the basic features, and analyzed the interaction of a set of such economies and the collective emerging dynamic. The topological structure of the economies' network appears to correlate with the collective properties observed. In particular, the strength of the coupling between the different networks as well as the specific connectivity of each node happen to play a crucial role in the determination of the final state.

Chemical communication and dynamics of droplet emulsions in networks of Belousov-Zhabotinsky micro-oscillators produced by microfluidics

Chemical communication leading to synchronization and collective behaviour of dynamic elements, such as cell colonies, is a widespread phenomenon with biological, physical and chemical importance. Such synchronization between elements proceeds via chemical communication by emmision, interdiffusion and reception of specific messenger molecules. On a lab scale, these phenomena can be modeled by encapsulating an oscillating chemical reaction, which serves as a signal (information) sender/receiver element, inside microcompartments such as droplet emulsions, liposomes and polymersomes. Droplets can thus be regarded as single units, able to generate chemical messengers that diffuse in the environment and hence can interact with other compartments. The Belousov-Zhabotinsky (BZ) reaction is a well-known chemical oscillator largely used as a model for complex nonlinear phenomena, including chemical, physical and biological examples. When the BZ-reaction is encapsulated inside microcompartments, its chemical intermediates can serve as messengers by diffusing among different microcompartments, to trigger specific reactions leading to a collective behavior between the elements. The geometry and constitution of the diffusion pathways play an important role in governing the collective behaviour of the system. In this context, microfluidics is not only a versatile tool for mastering the encapsulation process of the BZ-reaction in monodisperse microcompartments, but also for creating geometries and networks with well defined boundaries. The individual compartments can be engineered with selected properties using different surfactants in the case of simple emulsions, or with specific membrane properties in the case of liposomes. Furthermore, it enables the arrangement of these microcompartments in various geometric configurations, where the diffusive coupling pathways between individual compartments are both spatially and chemically well-defined. In this tutorial paper, we review a number of articles reporting various approaches to generate networks of compartmentalized Belousov-Zhabotinsky (BZ) chemical oscillators using microfluidics. In contrast to biological cellular networks, the dynamical characteristics of the BZ-reaction is well-known and, when confined in microcompartments arranged in different configurations with a pure interdiffusive coupling, these communicative microreactors can serve to mimic various types of bio-physical networks, aiding to comprehend the concept of chemical communication.

Noise-Induced and Control of Collective Behavior in a Population of Coupled Chemical Oscillators

Synchronization of intercommunicating individual oscillators is an important form of collective behavior used in nature as a mechanism to face dangers, act collectively, and communicate. The involvement of the medium where oscillators exist is an important ingredient. Because of their nature and their multiple different components, the medium and the environment are often perceived as stochastic relative to the deterministic nature of the individuals on some scale. This injects energy/matter into the system in ways that can enhance or de-enhance communication in a stochastic manner. Here we experimentally consider a large number of coupled nonlinear-chemical oscillators under the effect of a controlled normally distributed noise. Experiments show that the collective behavior of the oscillator is triggered by this stochastic perturbation, and we observe the dependence on the noise parameters. Our results point to the potential use of environmental fluctuations in determining the emergence and properties of collective behaviors in complex systems.

Synchronization patterns: from network motifs to hierarchical networks

We investigate complex synchronization patterns such as cluster synchronization and partial amplitude death in networks of coupled Stuart-Landau oscillators with fractal connectivities. The study of fractal or self-similar topology is motivated by the network of neurons in the brain. This fractal property is well represented in hierarchical networks, for which we present three different models. In addition, we introduce an analytical eigensolution method and provide a comprehensive picture of the interplay of network topology and the corresponding network dynamics, thus allowing us to predict the dynamics of arbitrarily large hierarchical networks simply by analysing small network motifs. We also show that oscillation death can be induced in these networks, even if the coupling is symmetric, contrary to previous understanding of oscillation death. Our results show that there is a direct correlation between topology and dynamics: hierarchical networks exhibit the corresponding hierarchical dynamics. This helps bridge the gap between mesoscale motifs and macroscopic networks.This article is part of the themed issue 'Horizons of cybernetical physics'.

Traveling phase waves in asymmetric networks of noisy chaotic attractors

We explore identical Rössler systems organized into two equally sized groups, among which differing positive and negative in- and out-coupling strengths are allowed. With this asymmetric coupling, we analyze patterns in the phase dynamics that coexist with chaotic amplitudes. We specifically investigate traveling phase waves where the oscillators settle on a new rhythm different from their own. We show that these waves are possible even without coherence in the phase angles. It is further demonstrated that the emergence of these incoherent traveling waves depends on the type of coupling, not on the individual dynamics of the Rössler systems. Together with the study of noise effects, our results suggest a promising new avenue toward the interplay of chaotic, noisy, coherent, and incoherent collective dynamics.

Synchronization of Coupled Oscillators on a Two-Dimensional Plane

The effect of the transfer rate of signal molecules on coupled chemical oscillators arranged on a two-dimensional plane was systematically investigated in this paper. A microreactor equipped with a surface acoustic wave (SAW) mixer was applied to adjust the transfer rate of the signal molecules in the microreactor. The SAW mixer with adjustable input powers provided a simple means to generate different mixing rates in the microreactor. A robust synchronization of the oscillators was found at an input radio frequency power of 20 dBm, with which the chemical waves were initiated at a fixed site of the oscillator system. With increasing input power, the frequency of the chemical waves was increased, which agreed well with the prediction given by the time-delayed phase oscillator model. Results from the finite element simulation agreed well with the experimental results.

Nonperfect mixing affects synchronization on a large number of chemical oscillators immersed in a chemically active time-dependent chaotic flow

The problem of synchronization of finite-size chemical oscillators described by active inertial particles is addressed for situations in which they are immersed in a reacting nonstationary chaotic flow. Active substances in the fluid will be modeled by Lagrangian particles closely following the fluid streamlines. Their interaction with the active inertial particles as well as the properties of the fluid dynamics will result in modifying the synchronization state of the chemical oscillators. This behavior is studied in terms of the exchange rate between the Lagrangian and inertial particles, and the finite-time Lyapunov exponents characterizing the flow. The coherence of the population of oscillators is determined by means of the order parameter introduced by Kuramoto. The different dynamics observed for the inertial particles (chemical oscillators) and Lagrangian particles (describing chemicals in the flow) lead to nonlinear interactions and patches of synchronized regions within the domain.

Phase-lag synchronization in networks of coupled chemical oscillators

Chemical oscillators with a broad frequency distribution are photochemically coupled in network topologies. Experiments and simulations show that the network synchronization occurs by phase-lag synchronization of clusters of oscillators with zero- or nearly zero-lag synchronization. Symmetry also plays a role in the synchronization, the extent of which is explored as a function of coupling strength, frequency distribution, and the highest frequency oscillator location. The phase-lag synchronization occurs through connected synchronized clusters, with the highest frequency node or nodes setting the frequency of the entire network. The synchronized clusters successively "fire," with a constant phase difference between them. For low heterogeneity and high coupling strength, the synchronized clusters are made up of one or more clusters of nodes with the same permutation symmetries. As heterogeneity is increased or coupling strength decreased, the phase-lag synchronization occurs partially through clusters of nodes sharing the same permutation symmetries. As heterogeneity is further increased or coupling strength decreased, partial synchronization and, finally, independent unsynchronized oscillations are observed. The relationships between these classes of behavior are explored with numerical simulations, which agree well with the experimentally observed behavior.

pH Oscillator Stretched in Space but Frozen in Time

Chemical oscillations are studied using a continuous-flow microfluidic system transforming the time domain of chemical oscillators into a spatial domain. This system allows one (i) to monitor the dynamics of chemical oscillators with the accuracy of vigorously stirred batch reactors but with the ease and speed of CSTRs and (ii) to rapidly screen the phase space of chemical oscillators in just one experiment versus a traditional series of batch measurements.