Aperiodic Behaviour of a Non-Linear Oscillator

Baker, N. H.; Moore, D. W.; Spiegel, E. A.

doi:10.1093/qjmam/24.4.391

Cited by 53 publications

(37 citation statements)

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“…(22) indicates that a sinusoidal solution exits for c * = − γ < 0, i.e., γ > , and * = 4B 1 ( − γ ) − 4A 2 1 < 0, and, in such a case,…”

Section: Analytical Solutions For α =mentioning

confidence: 99%

“…Third-order ordinary differential equations also appear in models of thermo-mechanical oscillators in fluids [22], transverse motions of piano strings [21], interactions between an elastic sphere and a surrounding fluid [20], vibrations of a mass attached to two horizontal strings and subject to aerodynamic forces [23], control systems [24,25], etc.…”

Section: Introductionmentioning

confidence: 99%

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Analytical and approximate solutions to autonomous, nonlinear, third-order ordinary differential equations

Ramos

2010

Nonlinear Analysis: Real World Applications

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“…(22) indicates that a sinusoidal solution exits for c * = − γ < 0, i.e., γ > , and * = 4B 1 ( − γ ) − 4A 2 1 < 0, and, in such a case,…”

Section: Analytical Solutions For α =mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analytical and approximate solutions to autonomous, nonlinear, third-order ordinary differential equations

Ramos

2010

Nonlinear Analysis: Real World Applications

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“…This is intuitively seen by examining Figure 1 (or Figure 3) [12] and Baker et al [1]. In this context, it is interesting to note that points on the strange invariant set can, to a certain extent, be characterized by a one-dimensional difference equation.…”

Section: Discussionmentioning

confidence: 89%

Analysis of the Lorenz Equations for Large r

Fowler

1984

Stud Appl Math

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In the limit of large r, the Lorenz equations become "almost" conservative. In this limit, one can use the method of averaging (or some equivalent) to obtain a set of two autonomous differential equations for two slowly varying amplitude functions B and D. A stable fixed point of these equations represents the stable periodic solution which is observed at large r. Tbere is an invariant line B = Don which the method breaks down and the averaged equations are no longer valid. In this paper we show how to extend the validity of the analysis by Poincare-mapping B and D across this line. This extended analysis provides (in principle) a complete recipe for constructing approximate solutions, and shows how astrange invariant set can occur in connection with an essentially analytically constructed two-dimensional mapping.

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“…Baker et al 1971), with a procedure very similar to the so-called Henyey technique (e.g., Henyey et al 1959; see also Christensen-Dalsgaard 2007) used in stellar modelling. The eigenvalue is then found by requiring that the remaining boundary condition, which effectively takes the role of Δ(σ ), be satisfied.…”

Section: The Relaxation Techniquementioning

confidence: 99%

ADIPLS—the Aarhus adiabatic oscillation package

Christensen‐Dalsgaard

2008

Astrophys Space Sci

369

148

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Development of the Aarhus adiabatic pulsation code started around 1978. Although the main features have been stable for more than a decade, development of the code is continuing, concerning numerical properties and output. The code has been provided as a generally available package and has seen substantial use at a number of installations. Further development of the package, including bringing the documentation closer to being up to date, is planned as part of the HELAS Coordination Action.

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Aperiodic Behaviour of a Non-Linear Oscillator

Cited by 53 publications

References 0 publications

Analytical and approximate solutions to autonomous, nonlinear, third-order ordinary differential equations

Analytical and approximate solutions to autonomous, nonlinear, third-order ordinary differential equations

Analysis of the Lorenz Equations for Large r

ADIPLS—the Aarhus adiabatic oscillation package

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