biosim3 - Linear Equations General Form: x n +1 = ax n + b...

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Unformatted text preview: Linear Equations General Form: x n +1 = ax n + b If b = 0, the equation is homogeneous If b 0, the equation is inhomogeneous Equilibrium , x e , is achieved if x n +1 = x n = x e . Linear discrete models have a single unique equilibrium if a , is not 1 . If a = 1 , then either there are no equilibria or all points are equilibria ( b = ). Stability: An equilibrium of a linear discrete model is stable if 1. Successive iterations of the model approach the equilibrium. 2. The slope | a | is less than 1 . LAST TIME Systems of Linear Difference Equations Sometimes you will be interested in two or more quantities that influence each others change from generation to generation. Systems of Linear Difference Equations Any system of linear first order difference equations can be converted to a single higher order system. This equation is 2nd order and requires two previous data points in order to determine the future value of x. Finding the Solution...
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biosim3 - Linear Equations General Form: x n +1 = ax n + b...

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