The Andronov–Hopf bifurcation with weakly oscillating parameters

Consideration is given to the problem of local bifurcations in neighborhoods of stationary states of dynamical systems with parameters evolving according to the periodic law. Scenarios of the bifurcation behavior of the system are studied and criteria for its stability are presented. It is shown that in the natural formulation, the Andronov–Hopf bifurcation of the dynamical system is transformed to a bifurcation of quasi-periodic oscillations. Asymptotic formulae are defined for occurring oscillations as well as recommendations for construction of solutions.