Related Experiment Videos
Numerical computation of orbits and rigorous verification of existence of snapback repellers
1Department of Applied Mathematics, National Chiayi University, Chiayi, Taiwan, 600, Republic of China. ccpeng@mail.ncyu.edu.tw
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.
Related Concept Videos
Circular Orbits and Critical Velocity for Satellites
Nicolaus Copernicus (1473-1543) first suggested that the Earth and all other planets orbit the Sun in...
Trigonometric Substitution
Net Change Theorem
Norton's Theorem
Critical Numbers and the Closed Interval Method
First Derivative Test: Problem Solving