Existence and stability of bifurcating tori in a neighborhood of an equilibrium position
The existence and stability of cycles and twodimensional tori bifurcating from the origin at an Hopf-Hopf-mode interaction with irrational frequency ratio is investigated. By normal form theory the system is reduced to two amplitude equations which are further simplified by coordinate changes. The stability of the bifurcating branches can be determined from the nonlinear parts at the critical parameter value. The procedure is demonstrated for examples with degenerate nonlinear terms.
Hopf-Hopf-mode interaction with irrational frequency ratio
scientific article; zbMATH DE number 4202770