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Unformatted text preview: pp. 878). THEOREM 3.3 The conditions 1 + a + b > , 1 a + b > , 1 b > are necessary and sufFcient for the equilibrium point of both homo-geneous and nonhomogeneous second-order difference equations to be asymptotically stable. 3.9 The logistic equation: discrete version Suppose y t + 1 = ay t by 2 t (3.21) where b is the competition coefcient. 7 Then y t + 1 = (1 + a ) y t by 2 t This is a nonlinear recursive equation and cannot be solved analytically as it stands. However, with a slight change we can solve the model. 8 Let y 2 t y t y t + 1 7 We shall discuss this coefcient more fully in chapter 14. 8 This approximate solution is taken from Grifths and Oldknow (1993, p. 16)....
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- Fall '11