Economics Dynamics Problems 237

Economics Dynamics Problems 237 - C9 $E$4*B8 The cells with...

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Discrete systems of equations 221 Figure 5.2. appreciate what is happening requires an understanding of the material in many of the chapters of this book. Consider the following nonlinear system, which is used to produce the H´enon map and which we shall investigate more fully in chapter 7. Example 5.9 The system is x t = 1 ax 2 t 1 + y t 1 y t = bx t 1 Our purpose here is not to investigate the properties of this system, but rather to see how we can display trajectories belonging to it. We begin with the spreadsheet, as shown in Fgure 5.3. We place the values of a and b in cells E3 and E4, where a = 1 . 4 and b = 0 . 3. In cells B8 and C8 we place the initial values for x and y , which are x 0 = 0 . 01 and y 0 = 0. The formulas for the two equations are placed in cells B9 and C9, respectively. These take the form B9 1-$E$3*B8^2+C8
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Unformatted text preview: C9 $E$4*B8 The cells with dollar signs indicate absolute addresses, while those without dollar signs indicate relative addresses. Cells B9 and C9 are then copied to the clipboard and pasted down. After blocking cells B8:C28 the graph wizard is then invoked and the resulting trajectory is shown in the inserted graph. The most conspicuous feature of this trajectory is that it does not have a ‘pattern’. In fact, given the parameter values there are two equilibrium points: ( x ∗ 1 , y ∗ 1 ) = ( − 1 . 1314 , − . 3394) and ( x ∗ 2 , y ∗ 2 ) = (0 . 6314 , . 1894), neither of which is approached within the Frst twenty periods. Why this is so we shall investigate in chapter 7....
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This note was uploaded on 12/14/2011 for the course ECO 3023 taught by Professor Dr.gwartney during the Fall '11 term at FSU.

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