Dynamical Chaos - Models and Experiments - Appearance Routes and Structure of Chaos in Simple Dynamical Systems

Anishchenko, Vadim Semonovich

doi:10.1142/9789812833693

Cited by 82 publications

(51 citation statements)

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“…The highest peak in its power spectrum ( figure 7(a)) occurs-as it should-at frequency f 1 = 0.2, with one harmonic at f 2 = 2f 1 . Note that the power spectrum of L 1 (figure 7(b)) still has dominant frequency components atf 1 = 0.1939 andf 2 = 0.3878 2f 1 , respectively close to f 1 and f 2 . This persistence of the peaks is due to intermittency of type I [50].…”

Section: Setting Of the Problem And Sketch Of Resultsmentioning

confidence: 93%

“…For related work, see [63] and references therein. On the other hand, the bifurcation diagram of (1) has been analysed in [55]. For other dynamical studies of this system, that we shall refer to as (autonomous) , see [36,43].…”

Section: The Driven Lorenz-84 Systemmentioning

confidence: 99%

“…The value of used in most of the numerical simulations is 0.5. However, smaller values will be used when investigating the relation between the dynamics of systems (2) and (1). For this reason is used as a control parameter together with F and G. We indicate the three-dimensional parameter space by M = {F, G, }.…”

Section: The Driven Lorenz-84 Systemmentioning

confidence: 99%

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Bifurcations and strange attractors in the Lorenz-84 climate model with seasonal forcing

2002

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A low-dimensional model of general circulation of the atmosphere is investigated. The differential equations are subject to periodic forcing, where the period is one year. A three-dimensional Poincaré mapping P depends on three control parameters F, G, and , the latter being the relative amplitude of the oscillating part of the forcing. This paper provides a coherent inventory of the phenomenology of P F,G, . For small, a Hopf-saddle-node bifurcation HSN of fixed points and quasi-periodic Hopf bifurcations of invariant circles occur, persisting from the autonomous case = 0. For = 0.5, the above bifurcations have disappeared. Different types of strange attractors are found in four regions (chaotic ranges) in {F, G} and the related routes to chaos are discussed.

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Section: Setting Of the Problem And Sketch Of Resultsmentioning

confidence: 93%

Section: The Driven Lorenz-84 Systemmentioning

confidence: 99%

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Bifurcations and strange attractors in the Lorenz-84 climate model with seasonal forcing

2002

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“…The projection of the phase trajectory to the plane the parameter values, where the limit cycles with a relatively large period become stable [15].…”

Section: Resultsmentioning

confidence: 99%

The Multiple Phase Slip Phenomena in the Narrow Superconducting Channels

2012

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The currentvoltage characteristic of the narrow superconducting channel is investigated by direct numerical integration of the time-dependent GinzburgLandau equations. We have demonstrated that the steps in the currentvoltage characteristic correspond to a number of dierent bifurcation points of the time-dependent GinzburgLandau equations. We have analytically estimated the period and the averaged voltage of the oscillating solution for the relatively small currents. We have also found the range of currents where the system transforms to the chaos.

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“…The system (1) has been studied in sufficient detail [9][10][11] and, despite simple circuitry and the form of the characteristic function (2), admits complex periodic, quasi-periodic, and chaotic oscillations in the absence of external action [8]. We will consider the set of control parameters for which the system exhibits multistability [9,10]: in the case of α = 1.5 and γ = 3.0, the system features oscillations with periods 7, 8, or 15, depending on the initial conditions.…”

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confidence: 99%