Resonances generate complicated bifurcation sequences. To design a picture of the bifurcation sequence occurring in the presence of a particular strong resonance, the two-parameters bifurcation of ... Thus, using knot theory, kneading theory and Hamiltonian bifurcation theory, we are able to connect a countable subsequence of “one-dimensional” bifurcations with a subsequence of “area-preserving” bifurcations in a two parameter family of suspensions in which horseshoes are created as the parameters vary. Jun 05, 2008 · In lineages using Sequence 3 (e.g., L.L1), where a domain (e.g., L.L1.A1 and.2) and daughter branches that form by planar bifurcation (e.g., L.L1.A and.P) lie in the same plane, domain branches could alternatively be interpreted as forming by highly asymmetric planar bifurcations in which one daughter branch of the bifurcation appears to form part of the domain and the other appears to be a continuation of the parent branch.

Thus, the Fibonacci sequence of 1, 2, 3, 5, 8, 13, and 21 can be found within the Mandelbrot set. Image gallery of a zoom sequence [ edit ] The Mandelbrot set shows more intricate detail the closer one looks or magnifies the image, usually called "zooming in". bifurcation, supercritical pitchfork bifurcation, subcritical pitchfork bifurcation, and Hopf bifurcation. In this first notebook, we look at a very simple linear system with a single parameters. As the parameter is changed, the equilibrium goes through the following sequence: saddle, stable node, stable spiral. We construct a movie of the