Economics Dynamics Problems 85

Economics Dynamics Problems 85 - f ( x )( x x ) = which...

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Continuous dynamic systems 69 Figure 2.19. Example 2.22 Consider ˙ x = f ( x ) = a ( x x ) 3 −∞ < x < , a > 0 There is a unique equilibrium at x = x = 0 which is globally stable. This is readily seen in terms of Fgure 2.19, which also displays the phase line. Now consider its linear approximation at x = x f ± ( x ) = 3 a ( x x ) 2 f ± ( x ) = 0 and so ˙ x = f ( x ) = f ( x ) +
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Unformatted text preview: f ( x )( x x ) = which does not exhibit global stability. This is because for any x = x then x = x for all t since x = 0. Consequently, x does not approach x in the limit, and so x = 0 cannot be asymptotically stable....
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