Stability in discrete population models
By: P. Cull and J. Chaffee.
Contributors: Chaffee, J.; Oregon State University. Dept. of Computer Science.
Series: [Technical report -- 99-20-01]; Technical report (Oregon State University. Dept. of Computer Science) -- 99-20-01.
Publisher: Oregon State University, Dept. of Computer Science
Published: 1999
Place of publication: [Corvallis, OR
Language: eng
Number of pages: 18
Subjects: Population -- Mathematical models.
Description: One dimensional nonlinear difference equations have been used to model population growth. The standard biological models have the interesting characteristic that they display global stability if they display local stability. Various researchers have sought a simple explanation for this agreement of local and global stability. Here, we show that enveloping by a linear fractional function is sufficient for global stability. We also show that for seven standard biological models local stability implies enveloping and hence global stability. We derive two methods to demonstrate enveloping and show that these methods can easily be applied to the seven example models.
Notes: Caption title.

Includes bibliographical references (leaves [17]-[18]).

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