Economics Dynamics Problems 102

Economics Dynamics Problems 102 - 86 Economic Dynamics As...

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Unformatted text preview: 86 Economic Dynamics As in the case of differential equations, if the dynamic system depends not only on h ( y t ) but also on t itself, then the system is said to be nonautonomous . If, however, the dynamic system is independent of t , then it is said to be autonomous . Hence, y t + 1 = t + 2 y t is a nonautonomous dynamic system, while y t + 1 = 2 y t is autonomous. Suppose we consider a linear first-order difference equation with all y-terms on the left-hand side, for example y t + 1 + ay t = g ( t ) If g ( t ) ≡ 0 for all t , then these equations are said to be homogeneous , otherwise they are nonhomogeneous . They are referred to as homogeneous difference equa- tions because if a series { y t } satisfies the equation, then so does the series { ky t } . Of particular importance is the order of a dynamic system. The dynamic system (3.1) is a first-order system in which each number in the sequence depends only on the previous number. In general, an m th-order discrete dynamic system takes...
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