On bifurcation into nonresonant quasi-periodic motions
Consider the autonomous system \(dz^ i/dt=Z^ i(z^ j;\eta^{\beta})\) where \(z^ i\) are the components of the state vector and the \(\eta^{\beta}\) are parameters. The paper is devoted to the study of the behaviour of the system in the vicinity of a coincident critical point characterized by Jacobian, which has two pairs of pure imaginary eigenvalues and all remaining eigenvalues have negative real parts. The stability, instability, and different types of bifurcation are studied. For simplicity it is assumed that the system is four-dimensional and involves only two independent parameters. An illustrative application to the electrical network is included.
scientific article; zbMATH DE number 4084113
scientific article