title: Numerical computation of orbits and rigorous verification of existence of snapback repellers.
abstract: 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.
authors.affiliation: Department of Applied Mathematics, National Chiayi University, Chiayi, Taiwan, 600, Republic of China. ccpeng@mail.ncyu.edu.tw
authors.forename: Chen-Chang
authors.initials: CC
authors.lastname: Peng
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D017711:Nonlinear Dynamics; D009716:Numerical Analysis, Computer-Assisted