Economics Dynamics Problems 131

# Economics Dynamics Problems 131 - (2 R = 1 In this instance...

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Discrete dynamic systems 115 Given y 0 and y 1 , it is possible to solve for c 1 and c 2 . SpeciFcally c 1 = y 0 c 2 = y 1 y 0 4 cos ± π 3 ² 4 sin ± π 3 ² If r and s are complex conjugate, then y n oscillates because the cosine function oscillates. There are, however, three different types of oscillation: (1) R > 1. In this instance the characteristic roots r and s lie outside the unit circle, shown in Fgure 3.15(a). Hence y n is oscillating, but increasing in magnitude. The system is unstable.
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Unformatted text preview: (2) R = 1. In this instance the characteristic roots r and s lie on the unit circle, and the system oscillates with a constant magnitude, Fgure 3.15(b). (3) R < 1. In this instance the characteristic roots r and s lie inside the unit circle and the system oscillates but converges to zero as n → ∞ , Fgure 3.15(c). The system is stable. Figure 3.15....
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