Generic Hopf bifurcation from lines of equilibria without parameters. I: Theory
Real autonomous systems of ordinary differential equations are considered having a line of equilibria and satisfying additional nondegeneracy conditions. The loss of stability along this line is investigated in cases of one real/a couple of complex conjugate eigenvalues crossing the imaginary axis. Based on the corresponding 2/3-dimensional normal forms the behavior of close trajectories is presented. The investigation of the problem is motivated by several applications.
scientific article; zbMATH DE number 1529992