Generic Hopf bifurcation from lines of equilibria without parameters. I: Theory (Q1585982)
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scientific article; zbMATH DE number 1529992
| Language | Label | Description | Also known as |
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| English | Generic Hopf bifurcation from lines of equilibria without parameters. I: Theory |
scientific article; zbMATH DE number 1529992 |
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Generic Hopf bifurcation from lines of equilibria without parameters. I: Theory (English)
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13 March 2001
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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.
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generic Hopf bifurcation
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line of equilibria
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nondegeneracy
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