Synchronization in Multiplex Leaky Integrate-and-Fire Networks With Nonlocal Interactions

Abstract

We study synchronization phenomena in a multiplex network composed of two rings with identical Leaky Integrate-and-Fire (LIF) oscillators located on the nodes of the rings. Within each ring the LIF oscillators interact nonlocally, while between rings there are one-to-one inter-ring interactions. This structure is motivated by the observed connectivity between the two hemispheres of the brain: within each hemisphere the various brain regions interact with neighboring regions, while across hemispheres each region interacts, primarily, with the functionally homologous region. We consider both positive (excitatory) and negative (inhibitory) linking. We identify numerically various parameter regimes where the multiplex network develops coexistence of active and subthreshold domains, chimera states, solitary states, full coherence or incoherence. In particular, for weak inter-ring coupling (weak multiplexing) different synchronization patterns on the two rings are supported. These are stable and are obtained when the intra-ring coupling values are near the critical points separating qualitatively distinct synchronization regimes, e.g., between the travelling fronts regime and the chimera state one.

The time-evolving epileptic brain network: concepts, definitions, accomplishments, perspectives

“…The majority of these models focuses on seizure dynamics (initiation, spread, termination) only, and the network character of the disease is only rarely taken into account ( Kalitzin et al, 2019 ; Goodfellow et al, 2022 ). Seizure-like events (states of synchronous rhythmic activity), however, may also emerge spontaneously—i.e., without a change in control parameters—from an oscillator network with some balance between regular and random topology ( Rothkegel and Lehnertz, 2014 ; Ansmann et al, 2016 ; Gerster et al, 2020 ; Anesiadis and Provata, 2022 ; Wu et al, 2022 ). Other mechanisms behind tipping phenomena include noise-, rate-, and shock-induced tipping [see, e.g., Ashwin et al (2012) ; Feudel et al (2018) ; Ritchie et al (2023) ; Swierczek-Jereczek et al (2023) ].…”

Chimera states in multiplex networks: Chameleon-like across-layer synchronization

“…The study of chimera states in multilayer networks showed from early on that couplings between network layers can induce or destabilize chimera states in individual layers [7][8][9][10][11][12][13]19,[21][22][23][24][25][26][27][28][29][30][31][32] .…”

“…Apart from ring networks [6][7][8][10][11][12][13][14][15][16][17][18][19][22][23][24][25][26][27][28][29] , two-dimensional lattices [30][31][32] with a multiplex inter-layer coupling were analyzed. Further studies addressed the role of coupling delays 12,[22][23][24][25] , inter-layer couplings with temporal fluctuations 10,27 , of limited duration 26 , and with nonlinear inertia 9 , as well as intra-layer coupling strengths adapting to the phase difference of interacting oscillators 21,33 .…”

“…tion between all oscillator pairs [6][7][8][9][10][11] two multiplexed rings can show alignment synchronization, for which the coherent domains attain the same 6,[14][15][16][17][18][19] or antipodal 19 positions on the rings of both layers. Generalized synchronization [37][38][39] can be induced by a driver-response inter-layer coupling in multiplexed rings 6 .…”

“…Motivated by this bridge to real-world dynamics, recent work analyzed chimera states in multilayer networks, revealing different across-layer synchronization types such as identical or almost identical [6][7][8][9][10][11] , generalized 6 , relay [11][12][13] , forced 14,15 , alignment 6,[14][15][16][17][18][19] , frequency 8 , and phase synchronization 20,21 . Are there relations between these different synchronization types?…”