An algorithm tracing out the tangent bifurcation curves and its application to duffing's equation
✍ Scribed by Hiroyuki Kitajima; Hiroshi Kawakami
- Publisher
- John Wiley and Sons
- Year
- 1996
- Tongue
- English
- Weight
- 364 KB
- Volume
- 79
- Category
- Article
- ISSN
- 1042-0967
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✦ Synopsis
The bifurcation diagram is constructed in the analysis of the bifurcation phenomenon. A problem in the conventional method of bifurcation diagram construction is that the computation is interrupted at the cusp point on the tangent bifurcation curve. Consequently, it has been necessary to determine the bifurcation set independently, excluding the cusp point, and then connect the curves afterward. This increases the time for constructing the bifurcation diagram when there exists a cusp point. Especially, when there exist multiple cusp points in the range where the parameter takes a small value, it has been almost impossibIe to trace the bifurcation curve.
From such a viewpoint, this paper proposes an algorithm based on the concept of the vector field, where the tangent bifurcation curve can be determined as a continuous curve, even if cusp points are included. The proposed algorithm is applied to the Duffing equation, and the result of computation is shown when the tangent bifurcation set including multiple cusp points is traced.