for the system

dx/dt= -vx+zy

dy/dt= -vy+(z-a)x

dz/dt= 1-xy

a,v are positive parameter.

after finding the fixed points, how am i supposed to classify them??

Should I build a 3*3 matrix??

If so, how am I supposed to take derivative, cuz there are non-linear turms like zy and xy????????????????

Thanks