Abstract
We present a new way of proving that a computer-generated orbit for the chaotic attractor outside the periodic windows of the quadratic map fa = ax (1 - x) can be shadowed for all time (i-e., there exist true orbits {xy}kj-1i=0 which stay near a numerical orbit {pi}Ni=0 for all time). This is done by computing a numerical orbit for a particular value of a and show that {pi}Ni=0 ≈ ∪mj=1 {xij}kj-1i=0 where Σmj=1 kj = N. The true orbits are found using slightly different maps fa, = ajx(1 - x), where max1≤j≤m (aj - a) < √δp. This technique can therefore be applied to other chaotic differential equation and discrete systems.
Original language | English (US) |
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Pages (from-to) | 117-129 |
Number of pages | 13 |
Journal | International Journal of Computer Mathematics |
Volume | 70 |
Issue number | 1 |
DOIs | |
State | Published - Jan 1 1998 |
Keywords
- Attractors
- Chaotic trajectories
- Quadratic map
- Shadowing
ASJC Scopus subject areas
- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics