A generalized two-disk dynamo model

Ershov, Sergey; Malinetskii, Georgii Gennadyevich; Ruzmaikin, A.

doi:10.1080/03091928908221824

Cited by 24 publications

(16 citation statements)

References 9 publications

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“…They found clear evidence of chaotic behaviour with vacillation accompanied by irregular reversals, and trajectories that approached Lorenz-like attractors in the phase space of the system. Ershov et al (1989) subsequently established the existence of a positive Lyapunov exponent and found that the attractor had a fractal dimension.…”

Section: Coupled Disc Dynamosmentioning

confidence: 97%

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Chaotic behaviour in low-order models of planetary and stellar dynamos

Weiss

2011

Geophysical & Astrophysical Fluid Dynamics

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The behaviour of the geodynamo and the solar cycle can be modelled by low-order systems of coupled nonlinear differential equations. The Earth's magnetic field reverses aperiodically, and similar behaviour is exhibited by disc dynamos that are described by the Lorenz equations. Chaotic behaviour is also a characteristic feature of coupled disc dynamos. In stars like the Sun, magnetic activity varies cyclically, with regular reversals of magnetic fields, but the cyclic activity is modulated on longer timescales. This behaviour can be described by normal form equations that account for symmetry-breaking as well as for variations in amplitude. The Von Ka´rma´n Sodium (VKS) experiment has successfully demonstrated magnetic reversals in the laboratory, and these results can be represented by evolution equations also.

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Section: Coupled Disc Dynamosmentioning

confidence: 97%

“…To proceed further, it becomes necessary to break the symmetry of (7a-d). This is most simply done by introducing different frictional drags, so that the equations become (Ershov et al 1989)…”

Section: Coupled Disc Dynamosmentioning

confidence: 99%

Chaotic behaviour in low-order models of planetary and stellar dynamos

Weiss

2011

Geophysical & Astrophysical Fluid Dynamics

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“…The dependence of ODEs (2) on parameters α, β, λ, κ was studied numerically and analytically by Hide and Moroz (1999). In the absence of the motor, the parameters β and λ are both equal to zero, and when κ also is equal to zero, Equations (2) describe the case of the famous homopolar dynamo discussed by Bullard (1955).…”

Section: The Model Of Secular Variationsmentioning

confidence: 99%

“…This system is described by three first-order ODEs only. Ershov, Malinetskii, and Ruzmaikin (1989) undertook a study of the generalized disc model. Hide (1997) extended the model and included both dissipation and energy deposition in the system, which consisted of one or several magnetically connected discs.…”

Section: Introductionmentioning

confidence: 99%

“TOY” Dynamo to Describe the Long-Term Solar Activity Cycles

Volobuev

2006

Sol Phys

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Secular variations of solar activity (Gleissberg and Suess cycles) have approximately 80 -130 and 200 year periods. They are manifested in both observed and proxy data. Here, we show that the basic dynamic features of the Schwabe cycle (asymmetry of its growth and decay phases) and secular cycles (multi-frequency structure and irregular Grand-extremes), as well as a connection between them, can be described by parameter tuning of the electromechanical "toy" dynamo system which has been widely used to model the inversions of the geomagnetic field. An amplitude-frequency diagram for the model magnetic flux has the same shape as the directly observed and reconstructed sunspot area indices.

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“…Показано, что в системе Рикитаки имеются инвариантные многообразия (предельные поверхности в R 4 ), на которые накручиваются фазовые траектории при достаточно длительном време-ни (рис. 3,5,7,9). При этом при одних начальных условиях после длительных осцилляций фазовая траектория сваливается на стационар, а при других начальных условиях фазо-вая траектория продолжает осциллировать (рис.…”

Section: заключениеunclassified

Visualization of phase trajectories of the Rikitake dynamic system

Potapov¹

2010

Nelin. Dinam.

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ГОУ ВПО Норильский индустриальный институт 663310, Россия, г. Норильск, ул. 50 лет Октября, д. 7PotapovVI@norvuz.ru Получено 10 января 2010 г.В статье проведено компьютерное исследование четырехмерной динамической системы Рикитаки с тремя параметрами, адекватно описывающей работу модели спаренных динамо с учетом вязкого терния. Показано, что в этой системе имеется пять состояний равновесия: четыре устойчивых фокуса-узла и одно седло (3, 1). Установлены бифуркации рождений пространственных перекрученных циклов, соответствующие удвоению периода колебаний динамической переменной и приводящие к хаотическим колебаниям при увеличении отно-шения коэффициентов трения.Ключевые слова: система Рикитаки, состояния равновесия, предельные циклы, хаос V. I. Potapov Visualization of phase trajectories of the Rikitake dynamic systemIn paper the computer research of four-dimensional dynamic system with three parameters adequately describing behavior of model coupled Dynamo in view of viscous friction is carried out. Is shown, that in this system there are five equilibrium states: four stable are focusesnode and one is saddle (3, 1). Are established the bifurcations of the spatial overwound cycles appropriate to doubling of the period of oscillations dynamic variable and resulting to chaotic oscillations at increase of the relation of factors friction.

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A generalized two-disk dynamo model

Cited by 24 publications

References 9 publications

Chaotic behaviour in low-order models of planetary and stellar dynamos

Chaotic behaviour in low-order models of planetary and stellar dynamos

“TOY” Dynamo to Describe the Long-Term Solar Activity Cycles

Visualization of phase trajectories of the Rikitake dynamic system

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