The nonbifurcation of periodic solutions when the variational matrix has a zero eigenvalue |
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| Authors: | HI Freedman |
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| Institution: | 1. Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1;2. Department of Mathematics, University of Minnesota, Minneapolis, Minnesota USA |
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| Abstract: | It is assumed that the variational matrix of the 2-dimensional system x′ = F(x, ?) has at least one zero eigenvalue rather than the usual Hopf assumption of two conjugate pure imaginary eigenvalues. It is then shown that genetically, although one may expect a bifurcation of stationary solutions, a bifurcation of periodic solutions will not occur. |
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