Eur. Phys. J. Special Topics 227, 1117–1128 (2018)
https://doi.org/10.1140/epjst/e2018-800073-7

Regular Article

Desynchronization by phase slip patterns in networks of pulse-coupled oscillators with delays

Desynchronization by phase slip patterns

¹ Institute of Applied Physics of the Russian Academy of Sciences, 46 Ul’yanov Street, 603950, Nizhny Novgorod, Russia
² German Aerospace Center (DLR), Institute of Transportation Systems, Rutherfordstraße 2, 12489 Berlin, Germany
³ Technical University of Berlin, Institute of Mathematics, Straße des 17. Juni 136, 10623 Berlin, Germany

^a e-mail: vladimir.klinshov@gmail.com

Received: 26 April 2018
Received in final form: 26 June 2018
Published online: 12 December 2018

Abstract

Coupling delays may cause drastic changes in the dynamics of oscillatory networks. In the present paper we investigate how coupling delays alter synchronization processes in networks of all-to-all coupled pulse oscillators. We derive an analytic criterion for the stability of synchrony and study the synchronization areas in the space of the delay and coupling strength. Specific attention is paid to the scenario of destabilization on the borders of the synchronization area. We show that in bifurcation points the system possesses homoclinic loops, which give rise to complex long- or quasi-periodic solutions. These newly born solutions are characterized by a synchronous group, from which an oscillator periodically escapes, laps one period, and rejoins. We call such a dynamical regime “phase slip patterns”.