"Cognitive" modes in small networks of almost identical chemical oscillators with pulsatile inhibitory coupling.

Abstract

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 Cinh of the perturbing pulses. At Cinh > Ccr, 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 Cinh. 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 Cinh. We demonstrate how the coupling between the BZ oscillators in these networks should be organized to find "cognitive" modes.