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. Diagrams of all rhythms found for three different types of connectivities (unidirectional on a ring, mutual on a ring, and all-to-all) are built in the plane C(inh)-τ, where C(inh) is the coupling strength. It is shown analytically and numerically that only four regular rhythms are stable for unidirectional coupling: walk (phase shift between spikes of neighbouring oscillators equals the quarter of the global period T), walk-reverse (the same as walk but consecutive spikes take place in the direction opposite to the direction of connectivity), anti-phase (any two neighbouring oscillators are anti-phase), and in-phase oscillations. In the case of mutual on the ring coupling, an additional in-phase-anti-phase mode emerges. For all-to-all coupling, two new asymmetrical patterns (two-cluster and three-cluster modes) have been found. More complex rhythms are observed at large C(inh), when some oscillators are suppressed completely or generate smaller number of spikes than others.
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.
Switching between stable oscillatory modes in a network of four Belousov–Zhabotinsky oscillators unidirectionally coupled in a ring analysed computationally and experimentally.
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