Bibliography & other sources

Keep in mind that this is a work in progress and the list may be modified.

ODEs and Non Linear Dynamics generalities

• Jordan, D., & Smith, P. (2007). Nonlinear ordinary differential equations (4th ed.). Oxford University Press.

Anharmonic Oscillators specifics

• B. R. Smith Jr., “The quadratically damped oscillator: A case study of a non-linear equation of motion”, American Journal of Physics 80, 816-824 (2012) https://doi.org/10.1119/1.4729440

• Hauko, R., & Repnik, R. (2019). Damped harmonic oscillation: Linear or quadratic drag force? In American Journal of Physics (Vol. 87, Issue 11, pp. 910–914). American Association of Physics Teachers (AAPT). https://doi.org/10.1119/1.5124978

• He, J.-H. (2019). The simpler, the better: Analytical methods for nonlinear oscillators and fractional oscillators. In Journal of Low Frequency Noise, Vibration and Active Control (Vol. 38, Issues 3–4, pp. 1252–1260). SAGE Publications. https://doi.org/10.1177/1461348419844145

• Holmes, P. (1979). A nonlinear oscillator with a strange attractor. In Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences (Vol. 292, Issue 1394, pp. 419–448). The Royal Society. https://doi.org/10.1098/rsta.1979.0068

• Kovacic, I., & Brennan, M. J. (Eds.). (2011). The Duffing Equation. Wiley. https://doi.org/10.1002/9780470977859

• Kouznetsov, D., Bisson, J.-F., Li, J., & Ueda, K. (2007). Self-pulsing laser as oscillator Toda: approximations through elementary functions. In Journal of Physics A: Mathematical and Theoretical (Vol. 40, Issue 9, pp. 2107–2124). IOP Publishing. https://doi.org/10.1088/1751-8113/40/9/016

• MAHMOUD, G. M., & BOUNTIS, T. (2004). THE DYNAMICS OF SYSTEMS OF COMPLEX NONLINEAR OSCILLATORS: A REVIEW. In International Journal of Bifurcation and Chaos (Vol. 14, Issue 11, pp. 3821–3846). World Scientific Pub Co Pte Lt. https://doi.org/10.1142/s0218127404011624

• Oyedeji, K. (2005). An analysis of a nonlinear elastic force van der Pol oscillator equation. Journal of Sound and Vibration, 281(1-2), 417–422. doi:10.1016/j.jsv.2004.03.040

Time Series

• Schelter, B., Winterhalder, M., & Timmer, J. (Eds.). (2006). Handbook of Time Series Analysis. Wiley. https://doi.org/10.1002/9783527609970

MCMC and Bayesian Inference

• The official emcee documentation. Link

• von Toussaint, U. (2011). Bayesian inference in physics. Reviews of Modern Physics (Vol. 83, Issue 3, pp. 943–999). American Physical Society (APS). https://doi.org/10.1103/revmodphys.83.943