Topic
Bifurcation diagram
About: Bifurcation diagram is a research topic. Over the lifetime, 8379 publications have been published within this topic receiving 139664 citations.
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TL;DR: In this paper, the bifurcation of steady-state solutions of a reaction-diffusion equation in one space variable was studied, and it was shown that S is never critical for any cubic polynomial.
251 citations
TL;DR: In this paper, a predator-prey system with one or two delays and a unique positive equilibrium is considered and its dynamics are studied in terms of the local stability of E∗ and of the description of the Hopf bifurcation that is proven to exist as one of the delays (taken as a parameter) crosses some critical values.
246 citations
TL;DR: In this article, a pseudospectral time-stepping formulation was adapted to enable stable and unstable steady states to be computed by Newton's method and linear stability analysis to be conducted by Arnoldi's method.
Abstract: Spherical Couette flow is studied with a view to elucidating the transitions between various axisymmetric steady‐state flow configurations. A stable, equatorially asymmetric state discovered by Buhler [Acta Mech. 81, 3 (1990)] consists of two Taylor vortices, one slightly larger than the other and straddling the equator. By adapting a pseudospectral time‐stepping formulation to enable stable and unstable steady states to be computed (by Newton’s method) and linear stability analysis to be conducted (by Arnoldi’s method), the bifurcation‐theoretic genesis of the asymmetric state is analyzed. It is found that the asymmetric branch originates from a pitchfork bifurcation; its stabilization, however, occurs via a subsequent subcritical Hopf bifurcation.
245 citations