Desynchronization induced by time-varying network

¹ Department of Physics, Lancaster University - Lancaster LA1 4YB, UK
² Dipartimento di Fisica e Astronomia, Università di Firenze, INFN and CSDC - Via Sansone 1, 50019 Sesto Fiorentino (FI), Italy
³ naXys, Namur Institute for Complex Systems, University of Namur - B5000 Namur, Belgium
⁴ Department of Mathematics, Royal Military Academy - B1000 Brussels, Belgium

^(a) m.lucas@lancaster.ac.uk
^(b) duccio.fanelli@gmail.com
^(c) timoteo.carletti@unamur.be
^(d) julien.petit@student.unamur.be

Received: 19 February 2018
Accepted: 12 April 2018

Abstract

The synchronous dynamics of an array of excitable oscillators, coupled via a generic graph, is studied. Non-homogeneous perturbations can grow and destroy synchrony, via a self-consistent instability which is solely instigated by the intrinsic network dynamics. By acting on the characteristic time-scale of the network modulation, one can make the examined system to behave as its (partially) averaged analogue. This result is formally obtained by proving an extended version of the averaging theorem, which allows for partial averages to be carried out. As a byproduct of the analysis, oscillation death is reported to follow the onset of the network-driven instability.