Solitary states in adaptive nonlocal oscillator networks

Berner, Rico; Polanska, Alicja; Schöll, Eckehard; Yanchuk, Serhiy

doi:10.1140/epjst/e2020-900253-0

Cited by 39 publications

(20 citation statements)

References 76 publications

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“…Heterogeneous dynamics, e.g., multifrequency clusters and tumor growth, may arise through the dynamic interaction of parenchymal cells, immune cells, and localized cytokine activity in a self-organized self-adaptive manner, even if the system parameters in the layers are chosen uniformly, i.e., homogeneous Berner et al (2019a), Berner et al (2020a). Heterogeneity can enter the parameters of oscillator networks in various ways.…”

Section: Methodology and Measuresmentioning

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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Section: Methodology and Measuresmentioning

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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“…They do not wander in space and mathematically, are Lyapunov stable states (standing waves) in the system phase space. Recently, the existence of the solitary states has been also reported in small networks [27], adaptive [29], multiplex [30], and power grid [15] systems, as well as in the mean-field limit [31].…”

Section: Introductionmentioning

confidence: 90%

Chimera states for directed networks

Jaros

Левченко

Kapitaniak

et al. 2021

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We demonstrate that chimera behavior can be observed in ensembles of phase oscillators with unidirectional coupling. For a small network consisting of only three identical oscillators (cyclic triple), tiny chimera islands arise in the parameter space. They are surrounded by developed chaotic switching behavior caused by a collision of rotating waves propagating in opposite directions. For larger networks, as we show for hundred oscillators (cyclic century), the islands merge into a single chimera continent which incorporates the world of chimeras of different configuration. The phenomenon inherits from networks with intermediate ranges of the unidirectional coupling and it diminishes as it decreases.

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“…Depending on the network and the specific dynamical system, various synchronization patterns with increasing complexity were explored [2][3][4][5]. Even in simple models of coupled oscillators, patterns such as complete synchronization [6,7], cluster synchronization [8][9][10][11], and various forms of partial synchronization have been found, such as frequency clusters [12], solitary [13][14][15], or chimera states [16][17][18][19][20]. In particular, synchronization is believed to play a crucial role in brain networks, for example, under normal conditions in the context of cognition and learning [21,22], and under pathological conditions, such as Parkinson's disease [23][24][25], epilepsy [26][27][28][29], tinnitus [30,31], schizophrenia, to name a few [32].…”

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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Solitary states in adaptive nonlocal oscillator networks

Cited by 39 publications

References 76 publications

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

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

Chimera states for directed networks

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

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