Awrejcewicz, J. Numerical investigations of the constant and periodic motions of the human vocal cords including stability and bifurcation phenomena. (English) Zbl 0694.34032 Dyn. Stab. Syst. 5, No. 1, 11-28 (1990). Summary: This paper presents a numerical approach to the systematic study of the behaviour of systems governed by autonomous nonlinear differential equations, such as the fifth-order system of equations of motion of the human vocal cords. Motions are traced, by changing the parameters, from steady state via Hopf bifurcations to periodic orbits. In certain intervals the character of the oscillations changes drastically when the parameters are varied slightly. Cited in 7 Documents MSC: 34C25 Periodic solutions to ordinary differential equations 65L99 Numerical methods for ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems 34D20 Stability of solutions to ordinary differential equations Keywords:autonomous nonlinear differential equations; equations of motion of the human vocal cords PDFBibTeX XMLCite \textit{J. Awrejcewicz}, Dyn. Stab. Syst. 5, No. 1, 11--28 (1990; Zbl 0694.34032) Full Text: DOI References: [1] DOI: 10.1007/978-3-642-48784-2_4 · doi:10.1007/978-3-642-48784-2_4 [2] Brommundt E., Proceedings of the International Conference of Nonlinear Vibrations pp 123– · Zbl 0323.73064 [3] DOI: 10.1007/978-1-4613-8159-4 · doi:10.1007/978-1-4613-8159-4 [4] Cronjaeger R., Die Entstehung des primären Stimmklangs im menschlichen Kehlkopf–ein Modell (1978) [5] DOI: 10.1007/978-1-4612-6400-2 · doi:10.1007/978-1-4612-6400-2 [6] DOI: 10.1007/978-1-4612-1140-2 · Zbl 0515.34001 · doi:10.1007/978-1-4612-1140-2 [7] Hale J. K., Ordinary Differential Equations (1969) · Zbl 0186.40901 [8] Hassard B. D., Theory and Applications of Hopf Bifurcation (1981) · Zbl 0474.34002 [9] DOI: 10.1016/0020-7225(83)90026-5 · Zbl 0502.73015 · doi:10.1016/0020-7225(83)90026-5 [10] DOI: 10.1115/1.3140693 · Zbl 0573.34036 · doi:10.1115/1.3140693 [11] Iakubovich V. A., Linear Differential Equations with Periodic Coefficients and their Application (1972) [12] DOI: 10.1007/978-1-4684-9336-8 · doi:10.1007/978-1-4684-9336-8 [13] Malkin I. G., Some Problems in the Theory of Nonlinear Oscillation (1956) · Zbl 0070.08703 [14] DOI: 10.1007/978-1-4612-6374-6 · doi:10.1007/978-1-4612-6374-6 [15] Nayfeh A. H., Introduction to Perturbation Techniques · Zbl 0449.34001 [16] DOI: 10.1016/0009-2509(87)87057-4 · doi:10.1016/0009-2509(87)87057-4 [17] DOI: 10.1016/0009-2509(87)85001-7 · doi:10.1016/0009-2509(87)85001-7 [18] DOI: 10.1137/1013063 · Zbl 0199.20503 · doi:10.1137/1013063 [19] DOI: 10.1016/0022-247X(66)90066-7 · Zbl 0196.49405 · doi:10.1016/0022-247X(66)90066-7 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.