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The parameterization by Draghilev method

The starting point is taken near the bifurcation point (0,0).

2 f X0 tmin tmax N DM.2 J ξ 1 el ξ 2 el f ξ 1 el diff ξ 1 el ξ 2 el f ξ 2 el diff 12 mat : t ξ D J 2 el - J 1 el 12 mat transpose J norme / : X0 tmin tmax N t ξ D rkfixed 31 line : 11 line

x y φ x 3^y 3^+ 31 0.1 a * - (* x * y * - : X0 1012 -^0 stack : a B1 x y φ X0 0 tmax tmax Δt / DM.2 : a B2 x y φ X0 0 t2max t2max Δt2 / DM.2 : 12 mat a d a B1 2 col a B1 3 col augment reverse a B2 2 col a B2 3 col augment stack : Plot a 06 range con a 1 + el a d eval : for con mat2sys.1 21 line : 51 line

tmax 1.5 - :

Δt 0.1 - :

t2max 6 :

Δt2 0.05 :

The parameterization by Draghilev method

Plot

x y φ x 2^y 2^+ (2^21 0.1 a * - (* x 3^3 x * y 2^* - (* - : X0 104 -^104 -^stack : a B x y φ X0 0 tmax tmax Δt / DM.2 : Plot a 06 range con a 1 + el a B 2 col a B 3 col augment eval : for con mat2sys.1 21 line : 41 line

tmax 13.3 :

Δt 0.05 :

The parameterization of Quiz functions by Draghilev method

Plot