Yoshifumi Takenouchi
Representation of period doubling by digraphs and characteristic polynomials.
Thu, 09/03/2009 - 17:38 — SomNambulAuthors: Yoshifumi Takenouchi, Richell Celeste
Subjects: Dynamical Systems
AbstractA general procedure which defines a partial ordering of cyclic permutations
induced by continuous maps is known for constructing immediate successors to a
cycle. We expound on this procedure in terms of labelled digraphs and
characteristic polynomials then apply this study to period doubling, the most
common route to chaos for a nonlinear dynamical system.Effect of the time delay on the stability and instability of the logistic map.
Fri, 08/28/2009 - 23:56 — SomNambulAuthors: Yoshifumi Takenouchi, Yasushi Ota
Subjects: Dynamical Systems
AbstractA proper discretization of the logistic differential equation, which is
preserving these two distinct equilibrium solutions and their unstability and
stability, suggest that we need to examine the time delay of the logistic map.
According to Murray, the effect of delay in models is "usually" to increase the
potential for instability. However the word "usually" is really ambiguous. In
this paper, we mathematically formulate and prove the two conjectures about
stability and instability.
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