Numerical computation of orbits and rigorous verification of existence of snapback repellers

In this paper we show how analysis from numerical computation of orbits can be applied to prove the existence of snapback repellers in discrete dynamical systems. That is, we present a computer-assisted method to prove the existence of a snapback repeller of a specific map. The existence of a snapba...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2007-03, Vol.17 (1), p.013107-013107
Main Author: Peng, Chen-Chang
Format: Article
Language:English
Subjects:
Algorithms
Computer Simulation
Nonlinear Dynamics
Numerical Analysis, Computer-Assisted
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Summary:In this paper we show how analysis from numerical computation of orbits can be applied to prove the existence of snapback repellers in discrete dynamical systems. That is, we present a computer-assisted method to prove the existence of a snapback repeller of a specific map. The existence of a snapback repeller of a dynamical system implies that it has chaotic behavior [F. R. Marotto, J. Math. Anal. Appl. 63, 199 (1978)]. The method is applied to the logistic map and the discrete predator-prey system.
ISSN:1054-1500
1089-7682
DOI:10.1063/1.2430907