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Imperfect transcritical and pitchfork bifurcations |
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| Authors: | Ping Liu Junping Shi Yuwen Wang |
| Affiliation: | a Y.Y. Tseng Functional Analysis Research Center and School of Mathematics and Computer Sciences, Harbin Normal University, Harbin, Heilongjiang 150025, PR China b School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, PR China c Department of Mathematics, College of William and Mary, Williamsburg, VA 23187-8795, USA |
| Abstract: | Imperfect bifurcation phenomena are formulated in framework of analytical bifurcation theory on Banach spaces. In particular the perturbations of transcritical and pitchfork bifurcations at a simple eigenvalue are examined, and two-parameter unfoldings of singularities are rigorously established. Applications include semilinear elliptic equations, imperfect Euler buckling beam problem and perturbed diffusive logistic equation. |
| Keywords: | Imperfect bifurcation Secondary bifurcation Bifurcation in Banach spaces |
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