Economics Dynamics Problems 71

Economics Dynamics Problems 71 - phase line . If x ± ( t )...

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Continuous dynamic systems 55 Figure 2.13. a variable which is a continuous function of time, t . Let x ± ( t ) denote an autonomous differential equation, so that x ± ( t ) is just a function of x and independent of t . Assume that we can solve for x ± ( t ) for any point in time t . Then at any point in time we have a value for x ± ( t ). The path of solutions as t varies is called a trajectory , path or orbit . The x -axis containing the trajectory is called the
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Unformatted text preview: phase line . If x ± ( t ) = 0 then the system is at rest. This must occur at some particular point in time, say t . The solution value would then be x ( t ) = x ∗ . The point x ∗ is referred to variedly as a rest point , fxed point , critical point , equilibrium point or steady-state solution . For the Malthusian population equation p ± ( t ) = kp , there is...
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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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