Gotsulenko, V.V. (2014) Self-Oscillations in Implicit Singularly Perturbed Dynamical Systems on the Plane. Nelineinaya Dinamika, 10, 157-175.
https://doi.org/10.20537/nd1402003

has been cited by the following article:

• TITLE: Self-Oscillations in a Generalized Van Der Pol and Rayleigh Oscillator

  AUTHORS: Borys I. Basok, Volodymyr V. Gotsulenko

  KEYWORDS: Self-Oscillations, Limit Cycle, Bifurcation, Wave Resistance

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.9, September 11, 2025

  ABSTRACT: This paper investigates the emergence and transformation of self-oscillatory regimes in a nonlinear dynamic system based on a generalized van der Pol oscillator model. Using asymptotic and bifurcation analysis, conditions for the existence of limit cycles are derived and their stability is examined. Special attention is given to both global and local bifurcations, including the formation of homoclinic loops and Andronov-Hopf bifurcations. The influence of wave resistance and equilibrium position on the qualitative structure of the phase portrait is also analyzed.