Van der Pol oscillator (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Van der Pol oscillator" in English language version.

refsWebsite

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18doi.org

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17worldcat.org

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9harvard.edu

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9semanticscholar.org

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7nih.gov

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6arxiv.org

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2archive.org

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2aps.org

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1bdtoolbox.org

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1oxfordjournals.org

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1scholarpedia.org

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1springer.com

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1siam.org

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1nytimes.com

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aip.org

scitation.aip.org

Lucero, Jorge C.; Schoentgen, Jean (2013). Modeling vocal fold asymmetries with coupled van der Pol oscillators. Proceedings of Meetings on Acoustics. Vol. 19. p. 060165. doi:10.1121/1.4798467. ISSN 1939-800X.

aps.org

journals.aps.org

Shah, Tirth; Chattopadhyay, Rohitashwa; Vaidya, Kedar; Chakraborty, Sagar (2015). "Conservative perturbation theory for nonconservative systems". Physical Review E. 92 (6): 062927. arXiv:1512.06758. Bibcode:2015PhRvE..92f2927S. doi:10.1103/physreve.92.062927. PMID 26764794. S2CID 14930486.
Chattopadhyay, Rohitashwa; Shah, Tirth; Chakraborty, Sagar (2018). "Finding the Hannay angle in dissipative oscillatory systems via conservative perturbation theory". Physical Review E. 97 (6): 062209. arXiv:1610.05218. Bibcode:2018PhRvE..97f2209C. doi:10.1103/PhysRevE.97.062209. PMID 30011548. S2CID 51635019.

archive.org

A, Dorodnicyn A. (1947). "Asymptotic solution of van der Pol's equation". Prikl. Mat. Mech. (in Russian). 11: 313–328.
Dorodnicyn, A. A. Asymptotic solution of Van Der Pol's equation. NIST Research Library. National Bureau of Standards.

arxiv.org

Cartwright, Julyan H. E.; Eguíluz, Víctor M.; Hernández-García, Emilio; Piro, Oreste (1999). "Dynamics of Elastic Excitable Media". International Journal of Bifurcation and Chaos. 09 (11): 2197–2202. arXiv:chao-dyn/9905035. Bibcode:1999IJBC....9.2197C. doi:10.1142/s0218127499001620. ISSN 0218-1274. S2CID 9120223.
Shah, Tirth; Chattopadhyay, Rohitashwa; Vaidya, Kedar; Chakraborty, Sagar (2015). "Conservative perturbation theory for nonconservative systems". Physical Review E. 92 (6): 062927. arXiv:1512.06758. Bibcode:2015PhRvE..92f2927S. doi:10.1103/physreve.92.062927. PMID 26764794. S2CID 14930486.
Chattopadhyay, Rohitashwa; Shah, Tirth; Chakraborty, Sagar (2018). "Finding the Hannay angle in dissipative oscillatory systems via conservative perturbation theory". Physical Review E. 97 (6): 062209. arXiv:1610.05218. Bibcode:2018PhRvE..97f2209C. doi:10.1103/PhysRevE.97.062209. PMID 30011548. S2CID 51635019.
Chia, A.; Kwek, L. C.; Noh, C. (2020-10-16). "Relaxation oscillations and frequency entrainment in quantum mechanics". Physical Review E. 102 (4): 042213. arXiv:1711.07376. Bibcode:2020PhRvE.102d2213C. doi:10.1103/physreve.102.042213. ISSN 2470-0045. PMID 33212685. S2CID 224801468.
Walter, Stefan; Nunnenkamp, Andreas; Bruder, Christoph (2014-03-06). "Quantum Synchronization of a Driven Self-Sustained Oscillator". Physical Review Letters. 112 (9): 094102. arXiv:1307.7044. Bibcode:2014PhRvL.112i4102W. doi:10.1103/physrevlett.112.094102. ISSN 0031-9007. PMID 24655255. S2CID 7950471.
Lee, Tony E.; Sadeghpour, H. R. (2013-12-04). "Quantum Synchronization of Quantum van der Pol Oscillators with Trapped Ions". Physical Review Letters. 111 (23): 234101. arXiv:1306.6359. Bibcode:2013PhRvL.111w4101L. doi:10.1103/physrevlett.111.234101. ISSN 0031-9007. PMID 24476274. S2CID 33622111.

bdtoolbox.org

Heitmann, S., Breakspear, M (2017–2022) Brain Dynamics Toolbox. bdtoolbox.org doi.org/10.5281/zenodo.5625923

doi.org

Heitmann, S., Breakspear, M (2017–2022) Brain Dynamics Toolbox. bdtoolbox.org doi.org/10.5281/zenodo.5625923
Cartwright, M. L. (1960). "Balthazar Van Der Pol". Journal of the London Mathematical Society. s1-35 (3). Wiley: 367–376. doi:10.1112/jlms/s1-35.3.367. ISSN 0024-6107.
van der Pol, Balth. (1926). "On "relaxation-oscillations"". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 2 (11). Informa UK Limited: 978–992. doi:10.1080/14786442608564127. ISSN 1941-5982.
VAN DER POL, BALTH; VAN DER MARK, J. (1927). "Frequency Demultiplication". Nature. 120 (3019). Springer Science and Business Media LLC: 363–364. Bibcode:1927Natur.120..363V. doi:10.1038/120363a0. ISSN 0028-0836. S2CID 186244992.
FitzHugh, Richard (1961). "Impulses and Physiological States in Theoretical Models of Nerve Membrane". Biophysical Journal. 1 (6). Elsevier BV: 445–466. Bibcode:1961BpJ.....1..445F. doi:10.1016/s0006-3495(61)86902-6. ISSN 0006-3495. PMC 1366333. PMID 19431309.
Nagumo, J.; Arimoto, S.; Yoshizawa, S. (1962). "An Active Pulse Transmission Line Simulating Nerve Axon". Proceedings of the IRE. 50 (10). Institute of Electrical and Electronics Engineers (IEEE): 2061–2070. doi:10.1109/jrproc.1962.288235. ISSN 0096-8390. S2CID 51648050.
Cartwright, Julyan H. E.; Eguíluz, Víctor M.; Hernández-García, Emilio; Piro, Oreste (1999). "Dynamics of Elastic Excitable Media". International Journal of Bifurcation and Chaos. 09 (11): 2197–2202. arXiv:chao-dyn/9905035. Bibcode:1999IJBC....9.2197C. doi:10.1142/s0218127499001620. ISSN 0218-1274. S2CID 9120223.
Lucero, Jorge C.; Schoentgen, Jean (2013). Modeling vocal fold asymmetries with coupled van der Pol oscillators. Proceedings of Meetings on Acoustics. Vol. 19. p. 060165. doi:10.1121/1.4798467. ISSN 1939-800X.
Panayotounakos, D.E.; Panayotounakou, N.D.; Vakakis, A.F. (2003-09-01). "On the lack of analytic solutions of the Van der Pol oscillator". ZAMM. 83 (9). Wiley: 611–615. Bibcode:2003ZaMM...83..611P. doi:10.1002/zamm.200310040. ISSN 0044-2267. S2CID 120504403.
Verhulst, Ferdinand (1996). Nonlinear Differential Equations and Dynamical Systems. Universitext. Berlin, Heidelberg: Springer Berlin Heidelberg. doi:10.1007/978-3-642-61453-8. ISBN 978-3-540-60934-6.
Andersen, C. M.; Geer, James F. (June 1982). "Power Series Expansions for the Frequency and Period of the Limit Cycle of the Van Der Pol Equation". SIAM Journal on Applied Mathematics. 42 (3): 678–693. doi:10.1137/0142047. ISSN 0036-1399.
Zonneveld, J.A. (1966). "Periodic solutions of the Van der Pol equation". Indagationes Mathematicae (Proceedings). 69: 620–622. doi:10.1016/s1385-7258(69)50068-x. ISSN 1385-7258.
Shah, Tirth; Chattopadhyay, Rohitashwa; Vaidya, Kedar; Chakraborty, Sagar (2015). "Conservative perturbation theory for nonconservative systems". Physical Review E. 92 (6): 062927. arXiv:1512.06758. Bibcode:2015PhRvE..92f2927S. doi:10.1103/physreve.92.062927. PMID 26764794. S2CID 14930486.
Chattopadhyay, Rohitashwa; Shah, Tirth; Chakraborty, Sagar (2018). "Finding the Hannay angle in dissipative oscillatory systems via conservative perturbation theory". Physical Review E. 97 (6): 062209. arXiv:1610.05218. Bibcode:2018PhRvE..97f2209C. doi:10.1103/PhysRevE.97.062209. PMID 30011548. S2CID 51635019.
Chia, A.; Kwek, L. C.; Noh, C. (2020-10-16). "Relaxation oscillations and frequency entrainment in quantum mechanics". Physical Review E. 102 (4): 042213. arXiv:1711.07376. Bibcode:2020PhRvE.102d2213C. doi:10.1103/physreve.102.042213. ISSN 2470-0045. PMID 33212685. S2CID 224801468.
Walter, Stefan; Nunnenkamp, Andreas; Bruder, Christoph (2014-03-06). "Quantum Synchronization of a Driven Self-Sustained Oscillator". Physical Review Letters. 112 (9): 094102. arXiv:1307.7044. Bibcode:2014PhRvL.112i4102W. doi:10.1103/physrevlett.112.094102. ISSN 0031-9007. PMID 24655255. S2CID 7950471.
Lee, Tony E.; Sadeghpour, H. R. (2013-12-04). "Quantum Synchronization of Quantum van der Pol Oscillators with Trapped Ions". Physical Review Letters. 111 (23): 234101. arXiv:1306.6359. Bibcode:2013PhRvL.111w4101L. doi:10.1103/physrevlett.111.234101. ISSN 0031-9007. PMID 24476274. S2CID 33622111.
Cartwright, M. L.; Littlewood, J. E. (1945). "On Non-Linear Differential Equations of the Second Order: I. the Equation y¨ − k (1-y 2 )y˙ + y = b λk cos(λl + α), k Large". Journal of the London Mathematical Society. s1-20 (3). Wiley: 180–189. doi:10.1112/jlms/s1-20.3.180. ISSN 0024-6107.

harvard.edu

ui.adsabs.harvard.edu

VAN DER POL, BALTH; VAN DER MARK, J. (1927). "Frequency Demultiplication". Nature. 120 (3019). Springer Science and Business Media LLC: 363–364. Bibcode:1927Natur.120..363V. doi:10.1038/120363a0. ISSN 0028-0836. S2CID 186244992.
FitzHugh, Richard (1961). "Impulses and Physiological States in Theoretical Models of Nerve Membrane". Biophysical Journal. 1 (6). Elsevier BV: 445–466. Bibcode:1961BpJ.....1..445F. doi:10.1016/s0006-3495(61)86902-6. ISSN 0006-3495. PMC 1366333. PMID 19431309.
Cartwright, Julyan H. E.; Eguíluz, Víctor M.; Hernández-García, Emilio; Piro, Oreste (1999). "Dynamics of Elastic Excitable Media". International Journal of Bifurcation and Chaos. 09 (11): 2197–2202. arXiv:chao-dyn/9905035. Bibcode:1999IJBC....9.2197C. doi:10.1142/s0218127499001620. ISSN 0218-1274. S2CID 9120223.
Panayotounakos, D.E.; Panayotounakou, N.D.; Vakakis, A.F. (2003-09-01). "On the lack of analytic solutions of the Van der Pol oscillator". ZAMM. 83 (9). Wiley: 611–615. Bibcode:2003ZaMM...83..611P. doi:10.1002/zamm.200310040. ISSN 0044-2267. S2CID 120504403.
Shah, Tirth; Chattopadhyay, Rohitashwa; Vaidya, Kedar; Chakraborty, Sagar (2015). "Conservative perturbation theory for nonconservative systems". Physical Review E. 92 (6): 062927. arXiv:1512.06758. Bibcode:2015PhRvE..92f2927S. doi:10.1103/physreve.92.062927. PMID 26764794. S2CID 14930486.
Chattopadhyay, Rohitashwa; Shah, Tirth; Chakraborty, Sagar (2018). "Finding the Hannay angle in dissipative oscillatory systems via conservative perturbation theory". Physical Review E. 97 (6): 062209. arXiv:1610.05218. Bibcode:2018PhRvE..97f2209C. doi:10.1103/PhysRevE.97.062209. PMID 30011548. S2CID 51635019.
Chia, A.; Kwek, L. C.; Noh, C. (2020-10-16). "Relaxation oscillations and frequency entrainment in quantum mechanics". Physical Review E. 102 (4): 042213. arXiv:1711.07376. Bibcode:2020PhRvE.102d2213C. doi:10.1103/physreve.102.042213. ISSN 2470-0045. PMID 33212685. S2CID 224801468.
Walter, Stefan; Nunnenkamp, Andreas; Bruder, Christoph (2014-03-06). "Quantum Synchronization of a Driven Self-Sustained Oscillator". Physical Review Letters. 112 (9): 094102. arXiv:1307.7044. Bibcode:2014PhRvL.112i4102W. doi:10.1103/physrevlett.112.094102. ISSN 0031-9007. PMID 24655255. S2CID 7950471.
Lee, Tony E.; Sadeghpour, H. R. (2013-12-04). "Quantum Synchronization of Quantum van der Pol Oscillators with Trapped Ions". Physical Review Letters. 111 (23): 234101. arXiv:1306.6359. Bibcode:2013PhRvL.111w4101L. doi:10.1103/physrevlett.111.234101. ISSN 0031-9007. PMID 24476274. S2CID 33622111.

nih.gov

pubmed.ncbi.nlm.nih.gov

FitzHugh, Richard (1961). "Impulses and Physiological States in Theoretical Models of Nerve Membrane". Biophysical Journal. 1 (6). Elsevier BV: 445–466. Bibcode:1961BpJ.....1..445F. doi:10.1016/s0006-3495(61)86902-6. ISSN 0006-3495. PMC 1366333. PMID 19431309.
Shah, Tirth; Chattopadhyay, Rohitashwa; Vaidya, Kedar; Chakraborty, Sagar (2015). "Conservative perturbation theory for nonconservative systems". Physical Review E. 92 (6): 062927. arXiv:1512.06758. Bibcode:2015PhRvE..92f2927S. doi:10.1103/physreve.92.062927. PMID 26764794. S2CID 14930486.
Chattopadhyay, Rohitashwa; Shah, Tirth; Chakraborty, Sagar (2018). "Finding the Hannay angle in dissipative oscillatory systems via conservative perturbation theory". Physical Review E. 97 (6): 062209. arXiv:1610.05218. Bibcode:2018PhRvE..97f2209C. doi:10.1103/PhysRevE.97.062209. PMID 30011548. S2CID 51635019.
Chia, A.; Kwek, L. C.; Noh, C. (2020-10-16). "Relaxation oscillations and frequency entrainment in quantum mechanics". Physical Review E. 102 (4): 042213. arXiv:1711.07376. Bibcode:2020PhRvE.102d2213C. doi:10.1103/physreve.102.042213. ISSN 2470-0045. PMID 33212685. S2CID 224801468.
Walter, Stefan; Nunnenkamp, Andreas; Bruder, Christoph (2014-03-06). "Quantum Synchronization of a Driven Self-Sustained Oscillator". Physical Review Letters. 112 (9): 094102. arXiv:1307.7044. Bibcode:2014PhRvL.112i4102W. doi:10.1103/physrevlett.112.094102. ISSN 0031-9007. PMID 24655255. S2CID 7950471.
Lee, Tony E.; Sadeghpour, H. R. (2013-12-04). "Quantum Synchronization of Quantum van der Pol Oscillators with Trapped Ions". Physical Review Letters. 111 (23): 234101. arXiv:1306.6359. Bibcode:2013PhRvL.111w4101L. doi:10.1103/physrevlett.111.234101. ISSN 0031-9007. PMID 24476274. S2CID 33622111.

ncbi.nlm.nih.gov

FitzHugh, Richard (1961). "Impulses and Physiological States in Theoretical Models of Nerve Membrane". Biophysical Journal. 1 (6). Elsevier BV: 445–466. Bibcode:1961BpJ.....1..445F. doi:10.1016/s0006-3495(61)86902-6. ISSN 0006-3495. PMC 1366333. PMID 19431309.

nytimes.com

Colman, David (11 July 2011). "There's No Quiet Without Noise". New York Times. Retrieved 11 July 2011.

oxfordjournals.org

jlms.oxfordjournals.org

Cartwright, M. L. (1960). "Balthazar Van Der Pol". Journal of the London Mathematical Society. s1-35 (3). Wiley: 367–376. doi:10.1112/jlms/s1-35.3.367. ISSN 0024-6107.

scholarpedia.org

Kanamaru, T., "Van der Pol oscillator", Scholarpedia, 2(1), 2202, (2007).

semanticscholar.org

api.semanticscholar.org

VAN DER POL, BALTH; VAN DER MARK, J. (1927). "Frequency Demultiplication". Nature. 120 (3019). Springer Science and Business Media LLC: 363–364. Bibcode:1927Natur.120..363V. doi:10.1038/120363a0. ISSN 0028-0836. S2CID 186244992.
Nagumo, J.; Arimoto, S.; Yoshizawa, S. (1962). "An Active Pulse Transmission Line Simulating Nerve Axon". Proceedings of the IRE. 50 (10). Institute of Electrical and Electronics Engineers (IEEE): 2061–2070. doi:10.1109/jrproc.1962.288235. ISSN 0096-8390. S2CID 51648050.
Cartwright, Julyan H. E.; Eguíluz, Víctor M.; Hernández-García, Emilio; Piro, Oreste (1999). "Dynamics of Elastic Excitable Media". International Journal of Bifurcation and Chaos. 09 (11): 2197–2202. arXiv:chao-dyn/9905035. Bibcode:1999IJBC....9.2197C. doi:10.1142/s0218127499001620. ISSN 0218-1274. S2CID 9120223.
Panayotounakos, D.E.; Panayotounakou, N.D.; Vakakis, A.F. (2003-09-01). "On the lack of analytic solutions of the Van der Pol oscillator". ZAMM. 83 (9). Wiley: 611–615. Bibcode:2003ZaMM...83..611P. doi:10.1002/zamm.200310040. ISSN 0044-2267. S2CID 120504403.
Shah, Tirth; Chattopadhyay, Rohitashwa; Vaidya, Kedar; Chakraborty, Sagar (2015). "Conservative perturbation theory for nonconservative systems". Physical Review E. 92 (6): 062927. arXiv:1512.06758. Bibcode:2015PhRvE..92f2927S. doi:10.1103/physreve.92.062927. PMID 26764794. S2CID 14930486.
Chattopadhyay, Rohitashwa; Shah, Tirth; Chakraborty, Sagar (2018). "Finding the Hannay angle in dissipative oscillatory systems via conservative perturbation theory". Physical Review E. 97 (6): 062209. arXiv:1610.05218. Bibcode:2018PhRvE..97f2209C. doi:10.1103/PhysRevE.97.062209. PMID 30011548. S2CID 51635019.
Chia, A.; Kwek, L. C.; Noh, C. (2020-10-16). "Relaxation oscillations and frequency entrainment in quantum mechanics". Physical Review E. 102 (4): 042213. arXiv:1711.07376. Bibcode:2020PhRvE.102d2213C. doi:10.1103/physreve.102.042213. ISSN 2470-0045. PMID 33212685. S2CID 224801468.
Walter, Stefan; Nunnenkamp, Andreas; Bruder, Christoph (2014-03-06). "Quantum Synchronization of a Driven Self-Sustained Oscillator". Physical Review Letters. 112 (9): 094102. arXiv:1307.7044. Bibcode:2014PhRvL.112i4102W. doi:10.1103/physrevlett.112.094102. ISSN 0031-9007. PMID 24655255. S2CID 7950471.
Lee, Tony E.; Sadeghpour, H. R. (2013-12-04). "Quantum Synchronization of Quantum van der Pol Oscillators with Trapped Ions". Physical Review Letters. 111 (23): 234101. arXiv:1306.6359. Bibcode:2013PhRvL.111w4101L. doi:10.1103/physrevlett.111.234101. ISSN 0031-9007. PMID 24476274. S2CID 33622111.

siam.org

epubs.siam.org

Andersen, C. M.; Geer, James F. (June 1982). "Power Series Expansions for the Frequency and Period of the Limit Cycle of the Van Der Pol Equation". SIAM Journal on Applied Mathematics. 42 (3): 678–693. doi:10.1137/0142047. ISSN 0036-1399.

springer.com

link.springer.com

Verhulst, Ferdinand (1996). Nonlinear Differential Equations and Dynamical Systems. Universitext. Berlin, Heidelberg: Springer Berlin Heidelberg. doi:10.1007/978-3-642-61453-8. ISBN 978-3-540-60934-6.

worldcat.org

search.worldcat.org

Cartwright, M. L. (1960). "Balthazar Van Der Pol". Journal of the London Mathematical Society. s1-35 (3). Wiley: 367–376. doi:10.1112/jlms/s1-35.3.367. ISSN 0024-6107.
van der Pol, Balth. (1926). "On "relaxation-oscillations"". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 2 (11). Informa UK Limited: 978–992. doi:10.1080/14786442608564127. ISSN 1941-5982.
VAN DER POL, BALTH; VAN DER MARK, J. (1927). "Frequency Demultiplication". Nature. 120 (3019). Springer Science and Business Media LLC: 363–364. Bibcode:1927Natur.120..363V. doi:10.1038/120363a0. ISSN 0028-0836. S2CID 186244992.
FitzHugh, Richard (1961). "Impulses and Physiological States in Theoretical Models of Nerve Membrane". Biophysical Journal. 1 (6). Elsevier BV: 445–466. Bibcode:1961BpJ.....1..445F. doi:10.1016/s0006-3495(61)86902-6. ISSN 0006-3495. PMC 1366333. PMID 19431309.
Nagumo, J.; Arimoto, S.; Yoshizawa, S. (1962). "An Active Pulse Transmission Line Simulating Nerve Axon". Proceedings of the IRE. 50 (10). Institute of Electrical and Electronics Engineers (IEEE): 2061–2070. doi:10.1109/jrproc.1962.288235. ISSN 0096-8390. S2CID 51648050.
Cartwright, Julyan H. E.; Eguíluz, Víctor M.; Hernández-García, Emilio; Piro, Oreste (1999). "Dynamics of Elastic Excitable Media". International Journal of Bifurcation and Chaos. 09 (11): 2197–2202. arXiv:chao-dyn/9905035. Bibcode:1999IJBC....9.2197C. doi:10.1142/s0218127499001620. ISSN 0218-1274. S2CID 9120223.
Lucero, Jorge C.; Schoentgen, Jean (2013). Modeling vocal fold asymmetries with coupled van der Pol oscillators. Proceedings of Meetings on Acoustics. Vol. 19. p. 060165. doi:10.1121/1.4798467. ISSN 1939-800X.
Panayotounakos, D.E.; Panayotounakou, N.D.; Vakakis, A.F. (2003-09-01). "On the lack of analytic solutions of the Van der Pol oscillator". ZAMM. 83 (9). Wiley: 611–615. Bibcode:2003ZaMM...83..611P. doi:10.1002/zamm.200310040. ISSN 0044-2267. S2CID 120504403.
Andersen, C. M.; Geer, James F. (June 1982). "Power Series Expansions for the Frequency and Period of the Limit Cycle of the Van Der Pol Equation". SIAM Journal on Applied Mathematics. 42 (3): 678–693. doi:10.1137/0142047. ISSN 0036-1399.
Bender, Carl M. (1999). Advanced mathematical methods for scientists and engineers I : asymptotic methods and perturbation theory. Steven A. Orszag. New York, NY. ISBN 978-1-4757-3069-2. OCLC 851704808.{{cite book}}: CS1 maint: location missing publisher (link)
Grimshaw, R. (1993). Nonlinear ordinary differential equations. Boca Raton, Fla.: CRC Press. pp. 161–163. ISBN 0-8493-8607-1. OCLC 28275539.
Zonneveld, J.A. (1966). "Periodic solutions of the Van der Pol equation". Indagationes Mathematicae (Proceedings). 69: 620–622. doi:10.1016/s1385-7258(69)50068-x. ISSN 1385-7258.
Strogatz, Steven (2019). "Example 8.4.1". Nonlinear dynamics and chaos : with applications to physics, biology, chemistry, and engineering (2nd ed.). Boca Raton. ISBN 978-0-367-09206-1. OCLC 1112373147.{{cite book}}: CS1 maint: location missing publisher (link)
Chia, A.; Kwek, L. C.; Noh, C. (2020-10-16). "Relaxation oscillations and frequency entrainment in quantum mechanics". Physical Review E. 102 (4): 042213. arXiv:1711.07376. Bibcode:2020PhRvE.102d2213C. doi:10.1103/physreve.102.042213. ISSN 2470-0045. PMID 33212685. S2CID 224801468.
Walter, Stefan; Nunnenkamp, Andreas; Bruder, Christoph (2014-03-06). "Quantum Synchronization of a Driven Self-Sustained Oscillator". Physical Review Letters. 112 (9): 094102. arXiv:1307.7044. Bibcode:2014PhRvL.112i4102W. doi:10.1103/physrevlett.112.094102. ISSN 0031-9007. PMID 24655255. S2CID 7950471.
Lee, Tony E.; Sadeghpour, H. R. (2013-12-04). "Quantum Synchronization of Quantum van der Pol Oscillators with Trapped Ions". Physical Review Letters. 111 (23): 234101. arXiv:1306.6359. Bibcode:2013PhRvL.111w4101L. doi:10.1103/physrevlett.111.234101. ISSN 0031-9007. PMID 24476274. S2CID 33622111.
Cartwright, M. L.; Littlewood, J. E. (1945). "On Non-Linear Differential Equations of the Second Order: I. the Equation y¨ − k (1-y 2 )y˙ + y = b λk cos(λl + α), k Large". Journal of the London Mathematical Society. s1-20 (3). Wiley: 180–189. doi:10.1112/jlms/s1-20.3.180. ISSN 0024-6107.