Non-hyperbolic equilibrium points of non-linear system

Reference no: EM13123947

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.

Reference no: EM13123947

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