title: Influence of passive elements on the dynamics of oscillatory ensembles of cardiac cells.
abstract: In this paper we focus on the influence of passive elements on the collective dynamics of oscillatory ensembles. Two major effects considered are (i) the influence of passive elements on the synchronization properties of ensembles of coupled nonidentical oscillators and (ii) the influence of passive elements on the wave dynamics of such systems. For the first effect, it is demonstrated that the introduction of passive elements may lead to both an increase or decrease in the global synchronization threshold. For the second effect, it is also demonstrated that the steady state of the passive element is a key parameter which defines how this passive element affects the wave dynamics of the oscillatory ensemble. It was shown that for different values of this parameter, one can observe increase or decrease in wave propagation velocity and increase or decrease in synchronization frequency in oscillatory ensembles with the growth of influence of passive elements. The results are obtained for the models of cardiac cells dynamics as well as for the Bonhoeffer-Van der Pol model and are compared with data of real biological experiments.
authors.affiliation: Department of Control Theory, Nizhny Novgorod University, 603950 Nizhny Novgorod, Russia.
authors.forename: V S
authors.initials: VS
authors.lastname: Petrov
authors.forename: G V
authors.initials: GV
authors.lastname: Osipov
authors.forename: J A K
authors.initials: JA
authors.lastname: Suykens