What adaptive neuronal networks teach us about power grids

Berner, Rico; Yanchuk, Serhiy; Schöll, Eckehard

doi:10.1103/physreve.103.042315

Cited by 39 publications

(18 citation statements)

References 87 publications

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“…We note that, as it has been shown in Ref. 29, the phase oscillator models with inertia are a subclass of phase oscillator models with adaptivity. In particular, considering L = 0 in (26) completely resembles the finding for phase oscillator models with inertia in (13).…”

Section: Stability Of M-splay Statessupporting

confidence: 61%

“…In the following, we study the linear stability of generalized splay states in a globally coupled network of N coupled phase oscillators with inertia 25,26,28,29,75,76,78 of the form…”

Section: B Application To the Kuramoto-sakaguchi Model With Inertiamentioning

confidence: 99%

“…A famous representative of the class of phase oscillator models, the Kuramoto model, in which all oscillators are coupled in the "all-to-all" manner, has attracted much attention due to its simple form and mathematical tractability 11,12 . The Kuramoto model and its extensions have gained additional popularity through applications to real-world problems 2,[13][14][15][16] , including neuroscience [17][18][19][20][21][22] and power grids [23][24][25][26][27][28][29] . Despite the simple structure, the Kuramoto model can exhibit many different dynamical regimes [30][31][32] , and sophisticated methods have been developed for their analysis.…”

Section: Introductionmentioning

confidence: 99%

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Generalized splay states in phase oscillator networks

Berner,

Yanchuk,

Maistrenko

et al. 2021

Preprint

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Networks of coupled phase oscillators play an important role in the analysis of emergent collective phenomena. In this article, we introduce generalized m-splay states constituting a special subclass of phase-locked states with vanishing mth order parameter. Such states typically manifest incoherent dynamics, and they often create high-dimensional families of solutions (splay manifolds). For a general class of phase oscillator networks, we provide explicit linear stability conditions for splay states and exemplify our results with the well-known Kuramoto-Sakaguchi model. Importantly, our stability conditions are expressed in terms of just a few observables such as the order parameter or the trace of the Jacobian. As a result, these conditions are simple and applicable to networks of arbitrary size. We generalize our findings to phase oscillators with inertia and adaptively coupled phase oscillator models.

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Section: Stability Of M-splay Statessupporting

confidence: 61%

“…In the following, we study the linear stability of generalized splay states in a globally coupled network of N coupled phase oscillators with inertia 25,26,28,29,75,76,78 of the form…”

Section: B Application To the Kuramoto-sakaguchi Model With Inertiamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Generalized splay states in phase oscillator networks

Berner,

Yanchuk,

Maistrenko

et al. 2021

Preprint

Self Cite

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“…Various synchronization patterns are known such as cluster synchronization where the network splits into groups of synchronous elements Dahms et al (2012), or partial synchronization patterns such as chimera states where the system splits into coexisting domains of coherent (synchronized) and incoherent (desynchronized) states Kuramoto and Battogtokh (2002), Abrams and Strogatz (2004), Panaggio and Abrams (2015), Sawicki (2019), Schöll (2020), Schöll et al (2020). These patterns were also explored in adaptive networks Seliger et al (2002), Aoki and Aoyagi (2009), Timms and English (2014), Kasatkin et al (2017), Berner et al (2019b), Berner et al (2021b), Berner et al (2021d), and in particular in adaptive two-layer networks of phase oscillators Kasatkin and Nekorkin (2018), Berner et al (2020b). Moreover, the role of synchronization is an important aspect in the field of network physiology, where multi-component physiological systems continuously interact in an integrated network to coordinate their functions Bashan et al (2012), Ivanov and Bartsch (2014), Bartsch et al (2015), Moorman et al (2016), Lin et al (2016).…”

Section: Introductionmentioning

confidence: 99%

Modeling Tumor Disease and Sepsis by Networks of Adaptively Coupled Phase Oscillators

Sawicki

Berner

Löser³

et al. 2022

Front. Netw. Physiol.

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In this study, we provide a dynamical systems perspective to the modelling of pathological states induced by tumors or infection. A unified disease model is established using the innate immune system as the reference point. We propose a two-layer network model for carcinogenesis and sepsis based upon the interaction of parenchymal cells and immune cells via cytokines, and the co-evolutionary dynamics of parenchymal, immune cells, and cytokines. Our aim is to show that the complex cellular cooperation between parenchyma and stroma (immune layer) in the physiological and pathological case can be qualitatively and functionally described by a simple paradigmatic model of phase oscillators. By this, we explain carcinogenesis, tumor progression, and sepsis by destabilization of the healthy homeostatic state (frequency synchronized), and emergence of a pathological state (desynchronized or multifrequency cluster). The coupled dynamics of parenchymal cells (metabolism) and nonspecific immune cells (reaction of innate immune system) are represented by nodes of a duplex layer. The cytokine interaction is modeled by adaptive coupling weights between the nodes representing the immune cells (with fast adaptation time scale) and the parenchymal cells (slow adaptation time scale) and between the pairs of parenchymal and immune cells in the duplex network (fixed bidirectional coupling). Thereby, carcinogenesis, organ dysfunction in sepsis, and recurrence risk can be described in a correct functional context.

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“…This work introduces a methodology to study synchronization in adaptive networks with heterogeneous plasticity (adaptation) rules. As a paradigmatic system, we consider an adaptively coupled phase oscillator network [69][70][71][72][73][74][75], which is proven to be useful for predicting and describing phenomena occurring in more realistic and detailed models [76][77][78][79]. More specifically, in the spirit of the master stability function approach, we consider the synchronization problem as the interplay between network structure and a heterogeneous adaptation rule arising from distance-(or location-)dependent synaptic plasticity.…”

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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What adaptive neuronal networks teach us about power grids

Cited by 39 publications

References 87 publications

Generalized splay states in phase oscillator networks

Generalized splay states in phase oscillator networks

Modeling Tumor Disease and Sepsis by Networks of Adaptively Coupled Phase Oscillators

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

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