I've got the function $f_{i}(\phi) = \gamma_{i}+\sin(2\cdot \sin \phi)$ for $i = 1,2$ where $\gamma_1=0.01$ and $\gamma_2=0.02$

$\phi_{1}(0) = 0.1$ and $\phi_{2}(0) = 0.2$

$\dot{\phi_1} = f_1(\phi)+d\cdot \sin(\phi_2-\phi_1)$

$\dot{\phi_2} = f_2(\phi)+d\cdot \sin(\phi_1-\phi_2)$

where $d = 0.1$.

So there should be something for example the following table:

t     | ϕ1  | ϕ2
0.00  | 0.1 |0.2
0.01  | ... |...
0.02  | ... |...
...
100.00| ... | ...

And so using the received values it's needed to plot a graph by the coordinates

So the question is how to plot the function $\phi_2(\phi_1)$ on the the following graph using MATLAB? enter image description here


Solve instead

$$ \phi_1'(\phi_2) = \frac{f_1(\phi_1(\phi_2))+d\sin(\phi_1(\phi_2)-\phi_2)}{f_2(\phi_2)-d\sin(\phi_1(\phi_2)-\phi_2)} $$

with initial conditions $\phi_1(0.2)=0.1$