Topological Methods in the Problem of Bifurcation of Forced Oscillations in Two-Parameter Systems

Abstract The paper proposes new signs of bifurcation of forced oscillations in two-parameter dynamic systems, described by differential equations with periodic coefficients. The proposed signs and corresponding formulas are obtained on the basis of topological methods of research of nonlinear operator equations, namely, on the basis of the theory of rotation of vector fields and the method of parameter functionalization. Some applications are considered.

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