Unformatted text preview: x ∗ , if Ax = . If A is nonsingular, or det( A ) ±= 0, then the only solution is x ∗ = . The only critical point is at the origin. The solution function x = φ ( t ) satis±es the differential equations, and this shows the solution path in the phase plane. In terms of vectors, the situation is illustrated in ±gure 4.15. The ( x , y )plane denotes the phase plane and the origin is a critical point, ±xed point or equilibrium point. At time t = 0 we have x (0) = x and y (0) = y . At time t there is a vector with coordinates ( x ( t ) , y ( t )) and the movement of the system as time increases is indicated by the arrows along the solution path....
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 Fall '11
 Dr.Gwartney
 Economics, Critical Point, Cos, ax, Eigenvalue, eigenvector and eigenspace, c1 + c2, e−t sin

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