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Populations of certain unicellular organisms, such as suspensions of yeast in nutrient solutions, undergo transitions to coordinated activity with increasing cell density. The collective behavior is believed to arise through communication by chemical signaling via the extracellular solution. We studied large, heterogeneous populations of discrete chemical oscillators (approximately 100,000) with well-defined kinetics to characterize two different types of density-dependent transitions to synchronized oscillatory behavior. For different chemical exchange rates between the oscillators and the surrounding solution, increasing oscillator density led to (i) the gradual synchronization of oscillatory activity, or (ii) the sudden "switching on" of synchronized oscillatory activity. We analyze the roles of oscillator density and exchange rate of signaling species in these transitions with a mathematical model of the interacting chemical oscillators.

Chimera states occur spontaneously in populations of coupled photosensitive chemical oscillators. Experiments and simulations are carried out on nonlocally coupled oscillators, with the coupling strength decreasing exponentially with distance. Chimera states with synchronized oscillators, phase waves, and phase clusters coexisting with unsynchronized oscillators are analyzed. Irregular motion of the cores of asynchronous oscillators is found in spiral-wave chimeras.

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Experiments are performed in which a large number (approximately 10(4)) of relaxation oscillators are globally coupled through the concentration of chemicals in the surrounding solution. Each oscillator consists of a microscopic catalyst-loaded particle that displays oscillations in the concentrations of chemical species when suspended in catalyst-free Belousov-Zhabotinsky (BZ) reaction solution. In the absence of stirring, the uncoupled particles display a range of oscillatory frequencies. In the well-stirred system, oscillations appear in the surrounding solution for greater than a critical number density of particles (n(crit)). There is a growth in the amplitude of oscillations with increasing n, accompanied by a slight increase or no change in frequency. A model is proposed to account for the behavior, in which the transfer of activator and inhibitor to and from the bulk medium is considered for each particle. We demonstrate that the appearance and subsequent growth in the amplitude of oscillations may be associated with partial synchronization of the oscillators.

Spontaneous spatiotemporal wave activity occurs in groups of excitable particles for groups larger than a critical size. Experiments are carried out with particles loaded with the catalyst of the Belousov-Zhabotinsky reaction that are immersed in catalyst-free reaction mixture. The particles diffusively exchange activator and inhibitor species with the surrounding solution. All particles are nonoscillatory when separated from the other particles; however, target and spiral waves are exhibited in sufficiently large groups. A cellular particle model of the system also exhibits transitions from excitable steady state behavior to spatiotemporal wave activity with increasing group size.