Nonlinear resonances and transitions to chaotic dynamics of a driven magnetic moment

•The calculations of these sub-harmonic resonant curves, predict that the transitions to and from complex chaotic motion could be found using only two parameters.•Transitions to chaos are predicted quite accurately by the Melnikov bifurcation functions for sufficiently small f/a and α.•These Lyapuno...

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Veröffentlicht in:Journal of magnetism and magnetic materials Jg. 501; S. 166352
Hauptverfasser: Gibson, Cameron, Bildstein, Steve, Hartman, Jewell Anne Lee, Grabowski, Marek
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 01.05.2020
Elsevier BV
Schlagworte:
Bifurcations
Chaos theory
Horizontally driven pendulum
Lyapunov exponent
Magnetic fields
Magnetic moment
Magnetic moments
Mathematical analysis
Melnikov method
Nonlinear
Parameters
Thin film
Thin films
Time dependence
Melnikov method
Horizontally driven pendulum
Nonlinear
Lyapunov exponent
Magnetic moment
Thin film
ISSN:0304-8853, 1873-4766
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Zusammenfassung:•The calculations of these sub-harmonic resonant curves, predict that the transitions to and from complex chaotic motion could be found using only two parameters.•Transitions to chaos are predicted quite accurately by the Melnikov bifurcation functions for sufficiently small f/a and α.•These Lyapunov lines (cuts) show a strong connection between the sub-harmonic resonant curves and the numerically derived transitions to and from chaotic motion. We examine a magnetic moment subject to a static external magnetic field and a time dependent driving magnetic field. Taking the system in the highly anisotropic limit, like that of a thin film, we lower the complexity of the system so that it may be analyzed for transitions to chaos analytically using the Melnikov method. Guided by the calculation of the Melnikov bifurcation functions we computationally calculated the Lyapunov characteristic exponents for several lines in parameter space and find that the Melnikov method is a good predictor of chaotic motion for sufficiently small external fields. Motion plots and Poincaré sections are also plotted for several parameter space points to observe the transitions to and from chaos around the calculated Melnikov bifurcations functions.
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ISSN:0304-8853
1873-4766
DOI:10.1016/j.jmmm.2019.166352