Solitary states in a 2D lattice of bistable elements with global and close to global interaction

Shepelev, Igor A.; Вадивасова, Т. Е.

doi:10.20537/nd1703002

Cited by 5 publications

(2 citation statements)

References 13 publications

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“…Например, в первом наблюдается периодическая, во втором хаотическая динамика. Надо заметить, что схожие пространственные режимы известны для систем связанных бистабильных осцилляторов: кольцо из осцилляторов ФитцХумо-Нагумо [17] или кубических отображений [18,19]. В этих моделях при определенных условиях возможна ситуация, когда динамика первого кластера соответствует первому потенциальному состоянию, а второго другому состоянию бистабильного осциллятора.…”

Section: примеры режимов динамикиunclassified

“…динамика этих субпопуляций оказывается несвязанной. Отдельного внимания заслуживает режимы C 6 представленные довольно нерегулярными одиночными выбросами численностей, которые в подобных системах называют уединенными состояниями [19,25]. Они примечательны своим довольно случайным расположением на решетке и амплитудой, которая, как правило, много выше, чем у остальных элементов.…”

Section: сложные пространственные структуры модели (4)unclassified

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Modeling the Spatio-Temporal Dynamics of a Population with Age Structure and Long-Range Interactions: Synchronization and Clustering

Кулаков¹,

Frisman²

2019

Math.Biol.Bioinf.

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The paper proposed a mathematical model for spatio-temporal dynamics of two-age populations coupled by migration living on a two-dimensional areal. The model equation is a system of nonlocal coupled two-dimensional maps. We considered cases when populations are coupled in a certain neighborhood of different form: circle, square or rhombus. Special attention is paid to the situation when the intensity of the migrants flow between the territories decreases with increasing distance between them. For this model we study the conditions for the formation of groups of synchronous populations or clusters that form, in space, typical structures like spots or stripes mixed with solitary states. It is shown that the dynamics, in time, of different clusters may differ significantly and may not be coherent and correspond to several simultaneous multistable regimes or potential states of the local population. Such spatio-temporal regimes are forced and are caused by impacts or perturbations on a single or several populations when their number falls into the attraction basin of another regime. With strong coupling, such clusters are rare and are represented by single outbursts or solitary states. However, the decrease in the coupling strength leads to the fact that these outbursts cause oscillations of their neighbors, and in their neighborhood a cluster of solitary states is formed which is surrounded by subpopulations with a different type of dynamics. It was found that the interaction of different type of clusters leads to the formation of a large number of groups with transitional dynamics that were not described for local populations.

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Section: примеры режимов динамикиunclassified

Section: сложные пространственные структуры модели (4)unclassified

Modeling the Spatio-Temporal Dynamics of a Population with Age Structure and Long-Range Interactions: Synchronization and Clustering

Кулаков¹,

Frisman²

2019

Math.Biol.Bioinf.

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Role of solitary states in forming spatiotemporal patterns in a 2D lattice of van der Pol oscillators

Shepelev

Bukh

Muni

et al. 2020

Chaos, Solitons & Fractals

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The behaviour of the ensemble of coupled van der Pol oscillators is abundant when coupling parameters are changed. Incoherent and chimeralike regimes are observed at small values of the coupling strength parameter. Synchronization takes place with increasing of the coupling strength and coupling range parameters. Various chimera and solitary states are realised when the coupling strength parameter is sufficiently large. The single van der Pol oscillator is taken in the regime of relaxation oscillations. Therefore, the lattice may realise spiral wave and spiral wave chimera regimes. Besides, target wave and solitary state regimes are observed in the ensemble. Finally, the solitary state and solitary state chimera regimes are firstly shown for the lattice of coupled van der Pol oscillators.

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Spatiotemporal patterns in a 2D lattice with linear repulsive and nonlinear attractive coupling

Shepelev

Muni

Вадивасова

2021

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We explore the emergence of a variety of different spatiotemporal patterns in a 2D lattice of self-sustained oscillators, which interact nonlocally through an active nonlinear element. A basic element is a van der Pol oscillator in a regime of relaxation oscillations. The active nonlinear coupling can be implemented by a radiophysical element with negative resistance in its current–voltage curve taking into account nonlinear characteristics (for example, a tunnel diode). We show that such coupling consists of two parts, namely, a repulsive linear term and an attractive nonlinear term. This interaction leads to the emergence of only standing waves with periodic dynamics in time and absence of any propagating wave processes. At the same time, many different spatiotemporal patterns occur when the coupling parameters are varied, namely, regular and complex cluster structures, such as chimera states. This effect is associated with the appearance of new periodic states of individual oscillators by the repulsive part of coupling, while the attractive term attenuates this effect. We also show influence of the coupling nonlinearity on the spatiotemporal dynamics.

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Solitary states in a 2D lattice of bistable elements with global and close to global interaction

Cited by 5 publications

References 13 publications

Modeling the Spatio-Temporal Dynamics of a Population with Age Structure and Long-Range Interactions: Synchronization and Clustering

Modeling the Spatio-Temporal Dynamics of a Population with Age Structure and Long-Range Interactions: Synchronization and Clustering

Role of solitary states in forming spatiotemporal patterns in a 2D lattice of van der Pol oscillators

Spatiotemporal patterns in a 2D lattice with linear repulsive and nonlinear attractive coupling

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