Economics Dynamics Problems 164

Economics Dynamics - 148 Economic Dynamics Figure 4.3 If a system has a fixed point(x∗ y∗ which is asymptotically stable and if every

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Unformatted text preview: 148 Economic Dynamics Figure 4.3. If a system has a fixed point (x∗ , y∗ ) which is asymptotically stable, and if every trajectory approaches the fixed point (i.e. both points close to the fixed point and far away from the fixed point), then the fixed point is said to be globally asymptotically stable. Another way to consider this is to establish the initial set of conditions for which the given fixed point is asymptotically stable, i.e., the largest ball from which any entering trajectory converges asymptotically to the fixed point. This set of initial conditions is called the basin of attraction. A fixed point is locally asymptotically stable if there exists a basin of attraction, Bε (x∗ , y∗ ), within which all trajectories entering this ball eventually approach the fixed point (x∗ , y∗ ). If the basin of attraction is the whole of the (x,y)-plane, then the system is globally asymptotically stable about the fixed point (x∗ , y∗ ). ...
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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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