EVALUATING BASINS OF ATTRACTION IN NON-LINEAR DYNAMICAL SYSTEMS USING AN IMPROVED RECURSIVE BOUNDARY ENHANCEMENT (RBE)
✍ Scribed by N.A. Alexander
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 355 KB
- Volume
- 209
- Category
- Article
- ISSN
- 0022-460X
No coin nor oath required. For personal study only.
✦ Synopsis
An improvement to the computational algorithm known as Recursive boundary enhancement (RBE) is described. This updated algorithm produces global stability phase space diagrams in periodically forced differential systems. These equations being derived from the dynamics of engineering structures with non-linear responses. The algorithm uses a process of boundary grid refinement to produce a greatly enhanced procedure which is accurate and less computationally expensive than the standard grid of starts (GOS) method. The algorithm focuses on the boundaries of the catchment basins which need the most attention. This concentration on the boundaries cannot be made in an a priori manner as the boundaries are initially unknown. While the algorithm is proceeding concepts of parent cells, child cells and cell division are used to determine the location of the boundaries. The role of cell neighbourhood comparison is modified, in the improved algorithm, to provide a handle to control accuracy and computational speed. The necessity for recursion in the algorithm is discussed. The procedure is valid for both non-fractal and fractal boundaries. A comparison of the old and new RBE algorithms and other methods such as GOS, SCM and ICM mapping methods are made to evaluate computational efficiency and accuracy.