Separation of fast and slow variables for a linear system by the method of multiple time scales

Wycoff, David; Balázs, N. L.

doi:10.1016/0378-4371(87)90229-9

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Perturbation Expansion Of the Solution1

Normal Form Calculation1

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2014

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Cited by 4 publications

(2 citation statements)

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“…The first two terms are the start of a Taylor expansion of the solution in powers of t, while the last term is an exponentially decaying transient. The initial value for the Taylor-expansion component, x 0 + ǫ(y 0 − kx 0 ), is just the initial value for the solution Q(t) on M. This result agrees with the previous two calculations of the initial condition Q(0), as we see by expanding (32) to give…”

Section: Perturbation Expansion Of the Solutionsupporting

confidence: 90%

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Initial conditions for models of dynamical systems

Cox

Roberts

1995

Physica D: Nonlinear Phenomena

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The long-time behaviour of many dynamical systems may be effectively predicted by a low-dimensional model that describes the evolution of a reduced set of variables. We consider the question of how to equip such a low-dimensional model with appropriate initial conditions, so that it faithfully reproduces the long-term behaviour of the original high-dimensional dynamical system. Our method involves putting the dynamical system into normal form, which not only generates the low-dimensional model, but also provides the correct initial conditions for the model. We illustrate the method with several examples.

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Section: Perturbation Expansion Of the Solutionsupporting

confidence: 90%

“…where f (ǫ) and g(ǫ) are constants. Wycoff & Balasz [32] have considered linear systems of a form that includes (21)(22), and have derived a substitution of the form ( 27) by considering a multiple-time-scale perturbation expansion.…”

Section: Normal Form Calculationmentioning

confidence: 99%