Unformatted text preview: orientation, the critical point is again an improper node that is stable. Had r > , then the critical point would be an improper node that is unstable. Case 4 (Complex roots, α ±= and β > ) In this case we assume the roots λ = r and λ = s are complex conjugate and with r = α + β i and s = α − β i , and α ±= 0 and β > 0. Systems having such complex roots can be expressed ˙ x = α x + β y ˙ y = − β x + α y...
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 Fall '11
 Dr.Gwartney
 Economics, Vector Space, Complex number, Economic Dynamics

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