Is it possible to draw a 2 parameter bifurcation diagram by hand or using only python? (without using software like AUTO) What would the steps involved be? How do you find the equation of a saddle node bifurcation line?
I want to reproduce a figure from a paper and I can't get my head around using AUTO so I would like to draw the figure by hand or using python.
I have not been able to find any good examples online for 2 parameter bifurcation diagrams.
Figure 2 from Chaotic Attractor in the Kuramoto model Maisstrenko 2005 This is the figure I am trying to reproduce.
These are the equations of the 2 dimensional system.
\begin{align*} \dot{\varphi}_1 &= \Delta_1+\frac{K}{3}[\sin(\varphi_2)-\sin(\varphi_1+\varphi_2)-2\sin(\varphi_1)] \\ \dot{\varphi}_2 &= \Delta_2+\frac{K}{3}[\sin(\varphi_1)-\sin(\varphi_1+\varphi_2)-2\sin(\varphi_2)] \end{align*}