Bifurcations of periodic solutions in autonomous nonlinear systems of weakly coupled equations are studied. A comparative analysis is carried out between the mechanisms of Lyapunov–Schmidt reduction of bifurcation equations for solutions close to harmonic oscillations and cnoidal waves. Sufficient conditions for the branching of orbits of solutions are formulated in terms of the Pontryagin functional depending on perturbing terms.
|Number of pages||10|
|Journal||Proceedings of the Steklov Institute of Mathematics|
|Publication status||Published - 1 Jan 2018|