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Economics Dynamics Problems 172

Economics Dynamics Problems 172 - 156 Economic Dynamics...

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156 Economic Dynamics Figure 4.13. II and then into I as it moves towards the fixed point. A similar behaviour occurs if the initial point is ( x 0 , y 0 ) = (3 , 1) beginning in quadrant III (see exercise 4). Once again the vector forces can be seen in terms of the direction field, which we show in figure 4.13, along with the equilibrium lines. 4.4 Matrix specification of autonomous systems The examples so far discussed illustrate that even with simple linear autonomous systems, the type of dynamic behaviour is quite varied. In order to pursue the sta- bility/instability aspects of systems of autonomous equations it is more convenient
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