Delay master stability of inertial oscillator networks

Börner, Reyk; Schultz, Pamela N.; Ünzelmann, Benjamin; Wang, Deli; Hellmann, Frank; Kurths, Jürgen

doi:10.1103/physrevresearch.2.023409

Cited by 8 publications

(8 citation statements)

References 34 publications

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“…The master stability approach for multiplex networks: General results. Since the introduction of the master stability approach [65], this methodology has been successfully used to describe the synchronization phenomena in complex networks [16,24,48] and is even today under constant investigation [13,18,56]. In [84,90], the master stability function for dynamical systems on multiplex networks was analyzed for a diffusive system of the form…”

Section: Applications Of the Multiplex Decompositionmentioning

confidence: 99%

The Multiplex Decomposition: An Analytic Framework for Multilayer Dynamical Networks

Berner¹,

Mehrmann²,

Schöll³

et al. 2021

SIAM J. Appl. Dyn. Syst.

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Multiplex networks are networks composed of multiple layers such that the number of nodes in all layers is the same and the adjacency matrices between the layers are diagonal. We consider the special class of multiplex networks where the adjacency matrices for each layer are simultaneously triagonalizable. For such networks, we derive the relation between the spectrum of the multiplex network and the eigenvalues of the individual layers. As an application, we propose a generalized master stability approach that allows for a simplified, low-dimensional description of the stability of synchronized solutions in multiplex networks. We illustrate our result with a duplex network of FitzHugh--Nagumo oscillators. In particular, we show how interlayer interaction can lead to stabilization or destabilization of the synchronous state. Finally, we give explicit conditions for the stability of synchronous solutions in duplex networks of linear diffusive systems.

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Section: Applications Of the Multiplex Decompositionmentioning

confidence: 99%

The Multiplex Decomposition: An Analytic Framework for Multilayer Dynamical Networks

Berner¹,

Mehrmann²,

Schöll³

et al. 2021

SIAM J. Appl. Dyn. Syst.

View full text Add to dashboard Cite

show abstract

“…The master stability approach for multiplex networks: general results. Since the introduction of the master stability approach [64], this methodology has been successfully used to describe the synchronization phenomena in complex networks [16,24,48] and is even today under constant investigation [13,18,55]. In [82,87], the master stability function for dynamical systems on multiplex networks was analyzed for a diffusive system of the form…”

Section: Applications Of the Multiplex Decompositionmentioning

confidence: 99%

“…One of the most powerful methodologies to study the synchronization on complex network structures is the master stability approach [64]. Since its introduction, this methodology has been further developed and extended [16,24,48,60] and is still under continuous investigation [13,18,42,55,57].…”

mentioning

confidence: 99%

The multiplex decomposition: An analytic framework for multilayer dynamical networks

Berner¹,

Mehrmann²,

Schöll³

et al. 2021

Preprint

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Multiplex networks are networks composed of multiple layers such that the number of nodes in all layers is the same and the adjacency matrices between the layers are diagonal. We consider the special class of multiplex networks where the adjacency matrices for each layer are commuting pairwise. For such networks, we derive the relation between the spectrum of the multiplex network and the eigenvalues of the individual layers. As an application, we propose a generalized master stability approach that allows for a simplified, low-dimensional description of the stability of synchronized solutions in multiplex networks. We illustrate our result with a duplex network of FitzHugh-Nagumo oscillators. In particular, we show how interlayer interaction can lead to stabilization or destabilization of the synchronous state. Finally, we give explicit conditions for the stability of synchronous solutions in duplex networks of linear diffusive systems.

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“…It greatly simplifies the problem by reducing the dimension and unifying the synchronization study for different networks. Since its introduction, the master stability approach has been extended and refined for various complex systems [34][35][36][37][38][39][40][41][42], and methods beyond the local stability analysis have been developed [43][44][45][46][47]. More recently, the master stability approach has been extended to another class of oscillator networks with high application potential, namely adaptive networks [48].…”

Section: Introductionmentioning

confidence: 99%

Synchronization in Networks With Heterogeneous Adaptation Rules and Applications to Distance-Dependent Synaptic Plasticity

Berner

Yanchuk

2021

Front. Appl. Math. Stat.

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This work introduces a methodology for studying synchronization in adaptive networks with heterogeneous plasticity (adaptation) rules. As a paradigmatic model, we consider a network of adaptively coupled phase oscillators with distance-dependent adaptations. For this system, we extend the master stability function approach to adaptive networks with heterogeneous adaptation. Our method allows for separating the contributions of network structure, local node dynamics, and heterogeneous adaptation in determining synchronization. Utilizing our proposed methodology, we explain mechanisms leading to synchronization or desynchronization by enhanced long-range connections in nonlocally coupled ring networks and networks with Gaussian distance-dependent coupling weights equipped with a biologically motivated plasticity rule.

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Delay master stability of inertial oscillator networks

Cited by 8 publications

References 34 publications

The Multiplex Decomposition: An Analytic Framework for Multilayer Dynamical Networks

The Multiplex Decomposition: An Analytic Framework for Multilayer Dynamical Networks

The multiplex decomposition: An analytic framework for multilayer dynamical networks

Synchronization in Networks With Heterogeneous Adaptation Rules and Applications to Distance-Dependent Synaptic Plasticity

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