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Generic Hopf bifurcation from lines of equilibria without parameters. I: Theory. (English) Zbl 0978.34035
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.

34C23 Bifurcation theory for ordinary differential equations
37G40 Dynamical aspects of symmetries, equivariant bifurcation theory
Full Text: DOI
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