Question:
Hyperbolic and non-hyperbolic equilibrium points
Please solve the following problem;
Consider the nonlinear system x' = f(x), where
f(x) = 1st row: x2 - x1
2nd row: kx1 - x2 - x1 x3
3rd row: x1 x2 - x3
a) For what values of k is the origin a hyperbolic equilibrium point of the system ? In this case, classify it as a sink, source or saddle.
b) For what values of k is the origin a Non-hyperbolic equilibrium point of the system ? In this case, determine the stability of the system at the origin.