1 research outputs found
Preservation of Takens-Bogdanov bifurcations for delay differential equations by Euler discretization
A new technique for calculating the normal forms associated with the map
restricted to the center manifold of a class of parameterized maps near the
fixed point is given first. Then we show the Takens-Bogdanov point of delay
differential equations is inherited by the forward Euler method without any
shift and turns into a 1:1 resonance point. The normal form near the 1:1
resonance point for the numerical discretization is calculated next by applying
the new technique to the map defined by the forward Euler method. The local
dynamical behaviors are analyzed in detail through the normal form. It shows
the Hopf point branch and the homoclinic branch emanating from the
Takens-Bogdanov point are shifted by the forward Euler method,
where is step size. At last, a numerical experiment is carried to
show the results.Comment: 17 pages, 4 figure