# In each of the Problems below, determine the critical point x = x⁰, and then classify its type and examine its stability by making the transformation x = x⁰ + u. 1. dx/ dt = [ 1 1 [ 2 x − 1 −1 ] 0 ] 2. dx/ dt = [ -2 1 [ -2 x − 1 −2 ] 1 ] 3. dx/ dt = [ -1 -1 [ -1 x − 2 −1 ] 5 ] 4. dx/ dt = [ 0 −β [ α x − α, β, γ, δ > 0 δ 0 ] −γ ]

###### Question:

In each of the Problems below, determine the critical point x = x⁰, and then classify its type and examine its stability by making the transformation x = x⁰ + u.
1. dx/ dt = [ 1 1 [ 2
x −
1 −1 ] 0 ]
2. dx/ dt = [ -2 1 [ -2
x −
1 −2 ] 1 ]
3. dx/ dt = [ -1 -1 [ -1
x −
2 −1 ] 5 ]
4. dx/ dt = [ 0 −β [ α
x − α, β, γ, δ > 0
δ 0 ] −γ ]

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