Abstract
The following Van der Pol and Holling-Tanner equations is analyzed from the qualitative viewpoint by investigating their vector fields and analyzing the nature of the stationary points of these equations. The winding numbers (indices) of the stationary points are investigated by calculating the Poincare integrals. This calculation is performed by a novel method which is based on application of the fast Fourier transform (FFT) formation to the Poincare integrand.
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