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Economics Dynamics Problems 170

# Economics Dynamics Problems 170 - 8 t i.e x 2 y 2 = φ t...

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154 Economic Dynamics Figure 4.9. Figure 4.10. of the system is clockwise. 3 This clockwise motion is shown most explicitly by including the direction Feld on the equilibrium lines, as shown in Fgure 4.10. Example 4.6 The two examples discussed so far both have Fxed points at the origin. How- ever, this need not always be the case. Consider the following system of linear 3 The nature of the trajectory can be established by noting that x 2 + y 2 = (9 e 2 t 1) 2 4 e 8 t + (1 + 9 e 2 t ) 2 4 e 8 t = 81 e 4 t + 1 2 e
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Unformatted text preview: 8 t i.e. x 2 + y 2 = φ ( t ) This is a circle at any moment in time whose radius is governed by φ ( t ). But over time the limit of φ ( t ) is zero. Consequently, as time passes the radius must diminish. This means that the trajectory conforms to a spiralling path of ever-decreasing radius. ±urthermore, the vector forces indicate that the spiral moves in a clockwise direction regardless of the initial value....
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