Global Asymptotic Stability in Some Discrete Dynamical Systems

For a discrete dynamical system xn+1=Txn on M⊂Rr some general conditions will be specified under which the unique equilibrium is globally asymptotically stable. As a special result we obtain the strong negative feedback property established in A. M. Amleh, N. Kruse, and G. Ladas (J. Differ. Equation...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 1999-07, Vol.235 (1), p.151-158
Main Authors: Kruse, Nicole, Nesemann, Tim
Format: Article
Language:English
Subjects:
difference equations
discrete dynamical systems
Exact sciences and technology
Finite differences and functional equations
Mathematical analysis
Mathematics
part-metric
Putnam equation
Sciences and techniques of general use
strong negative feedback property
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Summary:For a discrete dynamical system xn+1=Txn on M⊂Rr some general conditions will be specified under which the unique equilibrium is globally asymptotically stable. As a special result we obtain the strong negative feedback property established in A. M. Amleh, N. Kruse, and G. Ladas (J. Differ. Equations Appl. to appear). Finally we apply our result to show that the equilibrium x*=1 of the Putnam difference equation,xn+1=xn+xn−1+xn−2xn−3xnxn−1+xn−2+xn−3,with positive initial conditions x0,…,x−3 is globally asymptotically stable.
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.1999.6384