I want to classify the equilibrium points of a dynamic system.
For the system I found that the first one is the origin $(0,0)$ and also another $(\frac{5}{2},0) $ I worked with these two to see if my system is unstable or stable ( using the Jacobian , finding the eigenvalues .... ) everything was going right.
Here is the thing at the end when I checked with an online calculator to solve the system of equations to see if I didn't forget an equilibrium point. I did they say that there is also two others equilibrium point :
$(4,1+\sqrt5 i)$ and $(4,1-\sqrt5 i)$ my question is should I work with these two also to see if it's stable for this two points or equilibrium points can't be in $\mathbb C$ ?
I didn't see anything in my lecture about this or online anything would be really helpful! Thanks in advance.