Economics Dynamics Problems 202

Economics Dynamics Problems 202 - return to when we discuss...

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186 Economic Dynamics Figure 4.34. Example 4.19 (The Lorenz curve) The Lorenz equations are given by: dx dt = σ ( y x ) dy dt = rx y xz dz dt = xy bz (4.34) with parameter values σ = 10 , r = 28 , b = 8 / 3 and we take a step size of ± t = 0 . 01. In this example we take 2,000 steps, however Fgure 4.34 only shows the Frst few steps. In Fgure 4.35 we have three generated plots, (i) ( x , y ), (ii) ( x , z ) and (iii) ( y , z ). These diagrams illustrate what is referred to as strange attractors , a topic we shall
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Unformatted text preview: return to when we discuss chaos theory. 4.12 Solving systems of differential equations with Mathematica and Maple Chapter 2 sections 2.11 and 2.12 outlined how to utilise Mathematica and Maple to solve single differential equations. The method for solving systems of such equations is fundamentally the same. Consider the system, dx dt = f ( x , y , t ) dy dt = g ( x , y , t ) (4.35)...
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