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Summary: In the paper, a nonlinear analysis of RC phase‐shift oscillator with operational amplifier is done. Using Kirchhoff's laws, a nonlinear system of three differential equations that describes the behavior of the oscillator is obtained. This system is analyzed using the Poincaré–Andronov–Hopf bifurcation theory. The basic principles of the Poincaré–Andronov–Hopf bifurcation theory are presented in advance, including the Center Manifold Theory and the Theory of Normal Forms. It was found that, under certain conditions, the oscillator system has a limit cycle, which means that the oscillator under consideration generates periodic oscillations. The period, amplitude, and stability of the generated periodic oscillations are determined theoretically. The obtained analytical results are confirmed by a numerical analysis of the nonlinear system of differential equations performed by MATLAB. [ABSTRACT FROM AUTHOR]

The influence of intrapulse Raman scattering (IRS), self-steepening (SS) and third-order of dispersion (TOD) on the solutions of the complex cubic–quintic Ginzburg–Landau equation is studied by means of bifurcation analysis of the dynamical model. The numerical bifurcation diagram of the amplitude of the solution with respect to the nonlinear gain has revealed a cascade of bifurcations that leads to chaotic behaviour. We have found that the IRS leads to the larger shifts in positions and widths of the zones with different types of solutions in comparison to the influence of SS and TOD. Using numerical bifurcation diagrams of the amplitude of the solution with respect to the parameter describing IRS the following types of transformations have been identified: (a) from chaotic into two-periodic solution; (b) from two-periodic into a limit cycle; and (c) from a limit cycle into a stationary solution. [ABSTRACT FROM AUTHOR]