Geodesic
Structural Formulation and Self-Oscillation Prediction in Multidimensional Nonlinear Closed-Loop Autonomous Systems
International Journal of Applied Mathematics and Computer Science, Tome 9 (1999) no. 2, pp. 327-346.

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This paper describes the structure of a general two-dimensional nonlinear closed-loop system and application of the universal chart, leading to the use of computer graphics, for a systematic analysis of the complex problem of predicting self-oscillations (limit cycles). The graphical approach provides an explicit and novel insight into the conditions for the occurrence of limit cycles in such systems. This technique forms the basis of computer algorithms for predicting limit cycles in multidimensional nonlinear systems. Application of the technique has been illustrated through examples and comparison of results with digital simulation in MATLAB 4.0/SIMULINK 1.3.
Keywords: universal chart, phasor diagram, limit cycles, multidimensional, nonlinear system, describing function
Mots-clés : diagram, fazor, cykl graniczny, układ nieliniowy 
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     author = {Patra, K. C. and Pati, B. B. and {\L}ozowicki, A.},
     title = {Structural {Formulation} and {Self-Oscillation} {Prediction} in {Multidimensional} {Nonlinear} {Closed-Loop} {Autonomous} {Systems}},
     journal = {International Journal of Applied Mathematics and Computer Science},
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     number = {2},
     year = {1999},
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Patra, K. C.; Pati, B. B.; Łozowicki, A. Structural Formulation and Self-Oscillation Prediction in Multidimensional Nonlinear Closed-Loop Autonomous Systems. International Journal of Applied Mathematics and Computer Science, Tome 9 (1999) no. 2, pp. 327-346. http://geodesic.mathdoc.fr/item/IJAMCS_1999_9_2_a5/