Bifurcations of the Van der Pol–Duffing Oscillator

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PUŠENJAK, Rudolf .
Bifurcations of the Van der Pol–Duffing Oscillator. 
Strojniški vestnik - Journal of Mechanical Engineering, [S.l.], v. 49, n.7-8, p. 370-384, july 2017. 
ISSN 0039-2480.
Available at: <https://www.sv-jme.eu/article/bifurcations-of-the-van-der-pol-duffing-oscillator/>. Date accessed: 04 dec. 2021. 
doi:http://dx.doi.org/.
Pušenjak, R.
(2003).
Bifurcations of the Van der Pol–Duffing Oscillator.
Strojniški vestnik - Journal of Mechanical Engineering, 49(7-8), 370-384.
doi:http://dx.doi.org/
@article{.,
	author = {Rudolf  Pušenjak},
	title = {Bifurcations of the Van der Pol–Duffing Oscillator},
	journal = {Strojniški vestnik - Journal of Mechanical Engineering},
	volume = {49},
	number = {7-8},
	year = {2003},
	keywords = {incremental harmonic balance method; dynamical systems; nonlinear systems; bifurcation diagrams; },
	abstract = {The incremental harmonic balance method has proved to be an efficient tool for computing periodic oscillations in the analysis of nonlinear dynamical systems. It was developed into a form that enables the computing of steady-state periodic response with a dependence on various variable parameters. When the bifurcation process follows a sequence of period doublings, then the periodic response is composed of subharmonic solutions of higher orders. When no more subharmonic solutions exist in the process of periodic doublings, then the periodic response becomes chaotic. The changing of the amplitudes of the periodic oscillation in dependence of the variable system parameters and the possible transition into chaos is shown in bifurcation diagrams. A general procedure for the construction of a bifurcation diagram is the used in van der PolDuffing oscillator for various kinds of parameters. It is proved that the van der PolDuffing oscillator possesses various kinds of bifurcations, which can be analyzed by using suitable strategies.},
	issn = {0039-2480},	pages = {370-384},	doi = {},
	url = {https://www.sv-jme.eu/article/bifurcations-of-the-van-der-pol-duffing-oscillator/}
}
Pušenjak, R.
2003 July 49. Bifurcations of the Van der Pol–Duffing Oscillator. Strojniški vestnik - Journal of Mechanical Engineering. [Online] 49:7-8
%A Pušenjak, Rudolf 
%D 2003
%T Bifurcations of the Van der Pol–Duffing Oscillator
%B 2003
%9 incremental harmonic balance method; dynamical systems; nonlinear systems; bifurcation diagrams; 
%! Bifurcations of the Van der Pol–Duffing Oscillator
%K incremental harmonic balance method; dynamical systems; nonlinear systems; bifurcation diagrams; 
%X The incremental harmonic balance method has proved to be an efficient tool for computing periodic oscillations in the analysis of nonlinear dynamical systems. It was developed into a form that enables the computing of steady-state periodic response with a dependence on various variable parameters. When the bifurcation process follows a sequence of period doublings, then the periodic response is composed of subharmonic solutions of higher orders. When no more subharmonic solutions exist in the process of periodic doublings, then the periodic response becomes chaotic. The changing of the amplitudes of the periodic oscillation in dependence of the variable system parameters and the possible transition into chaos is shown in bifurcation diagrams. A general procedure for the construction of a bifurcation diagram is the used in van der PolDuffing oscillator for various kinds of parameters. It is proved that the van der PolDuffing oscillator possesses various kinds of bifurcations, which can be analyzed by using suitable strategies.
%U https://www.sv-jme.eu/article/bifurcations-of-the-van-der-pol-duffing-oscillator/
%0 Journal Article
%R 
%& 370
%P 15
%J Strojniški vestnik - Journal of Mechanical Engineering
%V 49
%N 7-8
%@ 0039-2480
%8 2017-07-07
%7 2017-07-07
Pušenjak, Rudolf.
"Bifurcations of the Van der Pol–Duffing Oscillator." Strojniški vestnik - Journal of Mechanical Engineering [Online], 49.7-8 (2003): 370-384. Web.  04 Dec. 2021
TY  - JOUR
AU  - Pušenjak, Rudolf 
PY  - 2003
TI  - Bifurcations of the Van der Pol–Duffing Oscillator
JF  - Strojniški vestnik - Journal of Mechanical Engineering
DO  - 
KW  - incremental harmonic balance method; dynamical systems; nonlinear systems; bifurcation diagrams; 
N2  - The incremental harmonic balance method has proved to be an efficient tool for computing periodic oscillations in the analysis of nonlinear dynamical systems. It was developed into a form that enables the computing of steady-state periodic response with a dependence on various variable parameters. When the bifurcation process follows a sequence of period doublings, then the periodic response is composed of subharmonic solutions of higher orders. When no more subharmonic solutions exist in the process of periodic doublings, then the periodic response becomes chaotic. The changing of the amplitudes of the periodic oscillation in dependence of the variable system parameters and the possible transition into chaos is shown in bifurcation diagrams. A general procedure for the construction of a bifurcation diagram is the used in van der PolDuffing oscillator for various kinds of parameters. It is proved that the van der PolDuffing oscillator possesses various kinds of bifurcations, which can be analyzed by using suitable strategies.
UR  - https://www.sv-jme.eu/article/bifurcations-of-the-van-der-pol-duffing-oscillator/
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	author = {Pušenjak, R.},
	title = {Bifurcations of the Van der Pol–Duffing Oscillator},
	journal = {Strojniški vestnik - Journal of Mechanical Engineering},
	volume = {49},
	number = {7-8},
	year = {2003},
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TY  - JOUR
AU  - Pušenjak, Rudolf 
PY  - 2017/07/07
TI  - Bifurcations of the Van der Pol–Duffing Oscillator
JF  - Strojniški vestnik - Journal of Mechanical Engineering; Vol 49, No 7-8 (2003): Strojniški vestnik - Journal of Mechanical Engineering
DO  - 
KW  - incremental harmonic balance method, dynamical systems, nonlinear systems, bifurcation diagrams, 
N2  - The incremental harmonic balance method has proved to be an efficient tool for computing periodic oscillations in the analysis of nonlinear dynamical systems. It was developed into a form that enables the computing of steady-state periodic response with a dependence on various variable parameters. When the bifurcation process follows a sequence of period doublings, then the periodic response is composed of subharmonic solutions of higher orders. When no more subharmonic solutions exist in the process of periodic doublings, then the periodic response becomes chaotic. The changing of the amplitudes of the periodic oscillation in dependence of the variable system parameters and the possible transition into chaos is shown in bifurcation diagrams. A general procedure for the construction of a bifurcation diagram is the used in van der PolDuffing oscillator for various kinds of parameters. It is proved that the van der PolDuffing oscillator possesses various kinds of bifurcations, which can be analyzed by using suitable strategies.
UR  - https://www.sv-jme.eu/article/bifurcations-of-the-van-der-pol-duffing-oscillator/
Pušenjak, Rudolf"Bifurcations of the Van der Pol–Duffing Oscillator" Strojniški vestnik - Journal of Mechanical Engineering [Online], Volume 49 Number 7-8 (07 July 2017)

Authors

Affiliations

  • University of Maribor, Faculty of Mechanical Engineering, Slovenia

Paper's information

Strojniški vestnik - Journal of Mechanical Engineering 49(2003)7-8, 370-384

The incremental harmonic balance method has proved to be an efficient tool for computing periodic oscillations in the analysis of nonlinear dynamical systems. It was developed into a form that enables the computing of steady-state periodic response with a dependence on various variable parameters. When the bifurcation process follows a sequence of period doublings, then the periodic response is composed of subharmonic solutions of higher orders. When no more subharmonic solutions exist in the process of periodic doublings, then the periodic response becomes chaotic. The changing of the amplitudes of the periodic oscillation in dependence of the variable system parameters and the possible transition into chaos is shown in bifurcation diagrams. A general procedure for the construction of a bifurcation diagram is the used in van der PolDuffing oscillator for various kinds of parameters. It is proved that the van der PolDuffing oscillator possesses various kinds of bifurcations, which can be analyzed by using suitable strategies.

incremental harmonic balance method; dynamical systems; nonlinear systems; bifurcation diagrams;