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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 = ( t ) satises 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