The Bifurcations and Chaotic Oscillations in Electric Circuits with Arc

Sydorets, Volodymyr

doi:10.1007/978-3-540-92203-2_3

Search citation statements

Order By: Relevance

Paper Sections

Select...

Qualitative Analysis Of Stationary Points In the Dynamic Sys...1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2014

2021

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…While crossing this manifold, the saddle-focus 𝑆 with a stable one-dimensional manifold can be transformed into a limiting cycle. In order to study the limiting cycle while going away from the neutral stability curve, the methods of qualitative and numerical analyses turn out rather effective [21].…”

Section: Qualitative Analysis Of Stationary Points In the Dynamic Sys...mentioning

confidence: 99%

Asymptotic Wave Solutions for the Model of a Medium with Van Der Pol Oscillators

Danylenko¹,

Skurativskyi²,

Skurativska³

2014

Ukr. J. Phys.

View full text Add to dashboard Cite

A one-dimensional mathematical model for a complex medium with van der Pol oscillators has been studied. Using the Bogolyubov-Mitropolsky method, the wave solutions for a weakly nonlinear model are derived, with their amplitudes being described by a three-dimensional dynamical system analyzed in more details by numerical and qualitative methods. In particular, periodic, multiperiodic, and chaotic trajectories are found in the phase space of the dynamical system. Bifurcations of those regimes were considered using the Poincaré section technique. Exact solutions are derived in the case where the three-dimensional system for amplitudes is reduced to the two-dimensional one. K e y w o r d s: nonlinear waves, van der Pol oscillator, chaotic attractor.

show abstract

Section: Qualitative Analysis Of Stationary Points In the Dynamic Sys...mentioning

confidence: 99%