Speaker: Bernold Fiedler (Institut für Mathematik, Freie Universität Berlin)
Time: 2026-02-27 15:30-17:30
Zoom Meeting ID: 892 9965 0777 Passcode: 127505
Abstract:
Standard bifurcation theory is concerned with families of vector fields involving one or several constant real parameters. The constant parameter provides a foliation of the total phase space. Frequently the presence of a trivial equilibrium manifold is also imposed.
Bifurcation without parameters, in contrast, discards the foliation by a constant parameter. Only the trivial equilibrium manifold is preserved. A rich dynamic phenomenology arises when normal hyperbolicity of the trivial equilibrium fails, due to zero or purely imaginary eigenvalues. Specifically, we address Hopf bifurcation and Takens-Bogdanov bifurcations, all in absence of parameters.
Examples include coupled oscillators, hyperbolic conservation and balance laws, plane Kolmogorov fluid flows, and G¨odel-Einstein cosmology of Bianchi type. The results are joint work with Andrei Afendikov, James C. Alexander, and Stefan Liebscher. See in particular Liebscher’s book:
Most recently, the results have significantly been extended by Jia Yuan Dai et al., to address a long-standing problem on chemostat oscillations under competition for nutrients.
About Speaker
Professor Bernold Fiedler is one of the foremost experts on Nonlinear Dynamical Systems, Bifurcation Theory, and their many applications to science and engineering. He has made several major contributions to these fields, including the introduction of the Homoclinic Index, the study of global bifurcations, and making many deep and important insights into reaction and diffusion equations (among other topics). In particular, Professor Fiedler is one of the leading experts on the connection between dynamical systems, analysis, bifurcations, and topology.
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