Dynamical regimes of four oscillators with excitatory pulse coupling. Issue 19 (4th May 2017) - Safonov, Dmitry A.; Klinshov, Vladimir V.; Vanag, Vladimir K.
Abstract : Dynamics of four almost identical chemical oscillators pulse coupled via excitatory coupling with time delays are systematically studied. Abstract : The dynamical regimes of four almost identical oscillators with pulsatile excitatory coupling have been studied theoretically with two models: a kinetic model of the Belousov–Zhabotinsky reaction and a phase-reduced model. Unidirectional coupling on a ring and all-to-all coupling have been considered. The time delay τ between the moments of a spike in one oscillator and a pulse perturbation of the other(s) plays a crucial role in the emergence of the dynamical modes, which are classified as regular, complex, and OS (oscillation-suppression)-modes. The regular modes, in which each oscillator gives only one spike during the period T, consist of the modes in which the period T is linearly dependent on τ and modes in which T is almost independent of τ . The τ -dependent and τ -independent modes alternate if τ increases. A unique sequence of modes observed at growing τ is the same for all types of connectivity and even for both excitatory and inhibitory coupling. For unidirectional coupling, the analytical dependence of T on τ is found for all regular modes. Multirhythmicity is observed at large values of the coupling strength C ex . The effect of small frequency dispersion (within a few percents) on the stability of the regular modes has been studied. Unusual modes like bursting or heteroclinic switching are found in narrow regions of the C ex – τ plane between the regular modes.