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The recursive sequence xn+1 = g(xn, xn−1)/(A + xn)

✍ Scribed by S. Stevo

Book ID
104349311
Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
188 KB
Volume
15
Category
Article
ISSN
0893-9659

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✦ Synopsis

In this note, we investigate the periodic character of solutions of the nonlinear, secondorder difference equation g(x~,x,-1) Xn+l =

A +xn

where the parameter A and the initial conditions x0 and xl are positive real numbers. We give sufficient conditions under which every positive solution of this equation converges to a period two solution. (~) 2002 Elsevier Science Ltd. All rights reserved.

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We study the global stability, the boundedness nature, and the periodic character of the positive solutions of the difference equation \[ x_{n+1}=\alpha+\beta x_{n-1} e^{-x_{n}} \quad, \quad n=0,1, \ldots \] which is interesting in its own right, but which may also be viewed as describing a popula