The limit cycle is associated in the Van der Pol oscillator with damping introduced to merely one of its state equations. In the present oscillator nonlinear damping is added to both equations. A unique behaviour is observed in spite of the smallness of the departure from the Van der Pol case. The present treatment is due to classical Poincaré-Bendixson and Liapunov methods. It illuminates in a surprisingly simple and elegant manner the great power of the methods.
Van der PolB., ‘Forced oscillations in a circuit with non-linear resistance (reception with reactive triode)’, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 3 (1927), 65–80.
3.
PavlidisP., Biological Oscillators: Their Mathematical Analysis (Academic Press, New York, 1973).
4.
LinkensD. A., ‘Analytical solution of large numbers of mutually coupled nearly sinusoidal oscillators’, IEEE Trans. Circ. Syst., 21 (1974), 294–300.
5.
DreitleinJ. and SmoesM. L., ‘A model for oscillatory kinetic systems’, J. Theor. Biol., 46 (1974), 559–572.
6.
GraemeJ. G., Operational Amplifiers: Design and Applications, (McGraw-Hill, New York, 1971), pp. 385–391.
7.
QiuShui-Sheng and FilanovskyI. M., ‘Periodic solutions of the Van der Pol equation with moderate values of damping coefficient’, IEEE Trans. Circ. Syst., 34 (1987), 913–918.
8.
FilanovskyI. M., ‘From delta function to oscillator amplitude stabilization’, Int. J. Elect. Enging. Educ., 37 (2000), 190–199.
9.
AggarwalJ. K., Notes on Nonlinear Systems (Van Nostrand Reinhold, New York, 1972).
10.
GrahamD. and McRuerD., Analysis of Nonlinear Control Systems (Dover, NewYork, 1971), pp. 450–469.
11.
GraemeJ. G., Applications of Operational Amplifiers: Third-Generation Techniques (McGraw-Hill, NewYork, 1973), pp. 150–154.
