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Numerical criterion for the duration of non-chaotic transients in ODEs

Szczebiot Ryszard, Kaczyński Roman, Gołdyn Leszek

Acta Mechanica et Automatica

2022

Vol. 16, no. 4

388--392

The paper proposes an original numerical criterion for the duration analysis of non-chaotic transients based on the Euclidean norm of a properly defined vector. For this purpose, transient trajectories, prior to their entering a small neighbourhood of the limit cycle, are used. The vector has been defined with its components constituting the lengths of the sections, which connect the origin of the coordinate system with appropriately determined transient trajectory points. The norm of the vector for the analysis of non-chaotic transients has also been applied. As an assessment criterion of transients, the convergence of the norm to small neighbourhood of the limit cycle with the assumed accuracy is used. The paper also provides examples of the application of this criterion to the Van der Pol oscillators in the case of periodic oscillations.

Criterion for transient behaviour in a nonlinear Duffing oscillator

Szczebiot Ryszard, Jordan Andrzej

Przegląd Elektrotechniczny

2019

R. 95, nr 4

196--199

The paper proposes a criterion for determining transient behaviour in a nonlinear Duffing oscillator. For this purpose studies of specific attractors typical of the system have been conducted. Exactly defined deviation value of ∆ with respect to the mean value of the surface areas bounded by the successive trajectory cycles has been assumed as the termination of the transient behaviour.

W pracy zaproponowano kryterium wyznaczania czasu trwania procesu przejściowego w nieliniowym oscylatorze Duffinga. W tym celu badano specyficzne atraktory charakteryzujące ten układ. Za kryterium końca procesu przejściowego przyjęto ściśle zdefiniowaną wartość odchyłki ∆ od wartości średniej pól powierzchni ograniczonych kolejnymi cyklami trajektorii.