My differential equation text book introduces a autonomous system given as follow:
$$x' = ax + by, y' = cx +dy$$
If $D = (a+d)^2 - 4(ad-bc) = 0$ and $a+d >0$, it says the equilibrium point to be degenerate repelling node.
What is the meaning of degenerate and node in this narrative? I know what we call repelling/attracting but can't understand these two terms without proper images or graphical description. (Book shows nothing but text only)
A node is an equilibrium point where the eigenvalues of the matrix $\pmatrix{a & b\cr c & d\cr}$ are real and all have the same sign. It is repelling if the eigenvalues are positive, attracting if they are negative. It is degenerate if there is only one eigenvalue. (Some texts reserve the term degenerate for the case where there is only one linearly independent eigenvector, the case of two linearly independent eigenvectors being called a singular node)
For pictures and descriptions of these and other types of equilibrium point, you might look at these notes of mine.