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Saddle node bifurcation at a nonhyperbolic limit cycle in a phase locked loop. (English) Zbl 0825.93302


MSC:

93C15 Control/observation systems governed by ordinary differential equations
93A30 Mathematical modelling of systems (MSC2010)
Full Text: DOI

References:

[1] Gardner, F. M., Phaselock Techniques (1979), John Wiley: John Wiley New York
[2] Lindsey, W. C., Synchronization Systems in Communication and Control (1972), Prentice Hall: Prentice Hall Englewood Cliffs, NJ
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[4] Stensby, J. L., False lock and bifurcation in the phase locked loop, SIAM J. Appl. Math., Vol. 47, No. 6, 1177-1184 (1987) · Zbl 0632.70022
[5] Coddington, E. A.; Levinson, N., Theory of Ordinary Differential Equations (1955), McGraw-Hill: McGraw-Hill New York · Zbl 0042.32602
[6] Hassard, B. D.; Wan, Y. H., Theory and Application of Hopf Bifurcation (1981), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0474.34002
[7] Andronov, A. A.; Leontovich, E. A.; Gordon, I. I.; Maier, A. G., Theory of Bifurcations of Dynamic Systems on a Plane (1973), John Wiley: John Wiley New York, (translated by D. Louvish) · Zbl 0282.34022
[8] Perko, L., Differential Equations and Dynamical Systems (1991), Springer: Springer New York · Zbl 0717.34001
[9] Ruelle, D., Elements of Differentiable Dynamics and Bifurcation Theory (1989), Academic Press: Academic Press New York · Zbl 0684.58001
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