Economics Dynamics Problems 61

Economics Dynamics Problems 61 - investigating a system of...

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Continuous dynamic systems 45 Figure 2.8. capital/labour ratio: one below the equilibrium level, another equal to the equi- librium level and a third above the equilibrium level. It is quite clear from the solution paths and the direction Feld that the equilibrium k is locally stable (see exercise 14). Direction Felds can usefully be employed for two further areas of study. ±irst, when considering nonlinear differential equations whose solution may not be avail- able. In this case the qualitative features of the solution can be observed from the direction Feld. Second, in the case of simultaneous equation systems, the exam- ples given so far refer to only one variable along with time. But suppose we are
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Unformatted text preview: investigating a system of two variables, say x and y , both of which are related to time. In these cases we can observe much about the solution trajectories from considering the direction Feld in the plane of x and y – which later we shall refer to as the phase plane . We shall investigate such differential equation systems in detail in chapter 4. 2.5 Separable functions Earlier we solved for the Frst-order linear homogeneous differential equation dx dt − kx = (2.18) for the initial condition x (0) = x (see equation (2.5)). We did this by Frst re-writing equation (2.18) in the form dx dt 1 x = k...
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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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