{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Economics Dynamics Problems 136

Economics Dynamics Problems 136 - very straightForward IF Î...

This preview shows page 1. Sign up to view the full content.

120 Economic Dynamics Figure 3.16. It is readily established that lim t →∞ y t = a b Three typical plots are shown in figure 3.16, for y 0 < a / b , y 0 = a / b and y 0 > a / b . Return to the original formulation y t + 1 y t = ay t by 2 t i.e. y t + 1 = (1 + a ) y t by 2 t It is not possible to solve this nonlinear equation, although our approximation is quite good (see exercise 6). But the equation has been much investigated by mathematicians because of its possible chaotic behaviour. 9 In carrying out this investigation it is normal to respecify the equation in its generic form x t + 1 = λ x t (1 x t ) (3.23) It is this simple recursive formulation that is often employed for investigation because it involves only a single parameter, λ . The reader is encouraged to set up this equation on a spreadsheet, which is
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: very straightForward. IF Î» = 3 . 2 it is readily established that the series will, aFter a suFfcient time period, oscillate between two values: a 1 = . 799455 and a 2 = . 513045. This two-cycle is typical oF the logistic equation For a certain range oF Î» . To establish the range oF Î» is straightForward but algebraically tedious. Here we shall give the gist oF the solution, and leave appendices 3.1 and 3.2 to illustrate how Mathematica and Maple , respectively, can be employed to solve the tedious algebra. Let f ( x ) = Î» x (1 âˆ’ x ) then a two-cycle result will occur iF a = f ( f ( a )) 9 We shall investigate chaos in chapter 7....
View Full Document

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business â€˜17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. Itâ€™s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania â€˜17, Course Hero Intern

• The ability to access any universityâ€™s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLAâ€™s materials to help me move forward and get everything together on time.

Jill Tulane University â€˜16, Course Hero Intern