A Chemical Neural Network and Collective Behavior in Globally Coupled Oscillators.
Abstract
The nervous system controls almost all actions in the body, and understanding its detailed structure and mechanism is one of the great challenges of science. Artificial neural networks have been modeled computationally to solve specific problems such as robot motion; however, few experimental studies have been designed to simulate biological neural networks because of the lack of experimental media with neural-like properties. An experimental network based on the photosensitive Belousov-Zhabotinsky reaction has been developed, in which the local excitability is controlled by light intensity. The spatiotemporal dynamics of these networks has been characterized, including sustained oscillations and collapse to the steady state. Here, we extend this work by incorporating the features of an actual network of neurons into the chemical system. Many oscillatory systems exist in nature, and they can form collective behavior due to the interactions between them. The simplest collective behavior of oscillators is phase or frequency synchronization. Two distinct types of transitions, the quorum sensing transition and the Kuramoto transition to synchronization have been observed in a globally coupled oscillator system. For the Kuramoto transition to synchronization, the oscillators are gradually synchronized as the number density increases at low coupling strength. For the quorum sensing transition to synchronization, at high coupling strength, the oscillators are quiescent if the number density is lower than a critical value, and synchronized oscillations suddenly switch on as the number density reaches the critical value. We have studied populations of ferroin-coated catalytic particles and have characterized the two types of transitions to synchronization as a function of the population density and coupling strength of the oscillators with the surrounding solution. Experimental studies of photochemical oscillators have shown more complex synchronization transitions compared to the ferroin-catalyzed oscillators. In this synchronization behavior, clusters of oscillators form in which frequency and phase are synchronized but with different phases for different phase clusters. Based on large populations of Ru(bpy[special characters omitted] catalyzed oscillators, we experimentally study the formation of phase clusters and their stability as a function of the density of the oscillators. We also simulate the cluster behavior based on the three-variable ZBKE model and compare our results with experiment.