Abstract
Unstable dimension variability is a mechanism whereby an invariant set of a dynamical system, like a chaotic attractor or a strange saddle, loses hyperbolicity in a severe way, with serious consequences on the shadowability properties of numerically generated trajectories. In dynamical systems possessing a variable parameter, this phenomenon can be triggered by the bifurcation of an unstable periodic orbit. This Letter aims at discussing the possible types of codimension-one bifurcations leading to unstable dimension variability in a two-dimensional map, presenting illustrative examples and displaying numerical evidences of this fact by computing finite-time Lyapunov exponents. (C) 2004 Elsevier B.V. All rights reserved.
Original language | English |
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Pages (from-to) | 244-251 |
Number of pages | 7 |
Journal | Physics Letters A |
Volume | 321 |
DOIs | |
Publication status | Published - 2004 |
Keywords
- COUPLED CHAOTIC SYSTEMS
- LYAPUNOV EXPONENTS
- PERIODIC-ORBITS
- SYNCHRONIZATION
- ATTRACTORS
- DYNAMICS
- SETS