“Cobweb” diagrams. Affine Difference Equations---Slope bigger than 1.

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Presentation transcript:

“Cobweb” diagrams

Affine Difference Equations---Slope bigger than 1

Affine Difference Equations---Slope less than -1

What if we start iterating with a point that lies to the left of the fixed point? Affine Difference Equations---Slope smaller than 1

Affine Difference Equations---Slope in (-1,0).

Affine Difference Equations---Slope equal to1

Conclusions: Long term behavior of solutions to affine difference equations: If, the sequence (A(n)), n = 1, 2, 3,... “blows up”. That is, The fixed point is a repelling fixed point. If, the sequence (A(n)), n = 1, 2, 3,... Converges to the fixed point of the function. That is, The fixed point is an attracting fixed point.