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Complex Bifurcation from Real Paths

Henderson, M. E. and Keller, H. B. (1990) Complex Bifurcation from Real Paths. SIAM Journal on Applied Mathematics, 50 (2). pp. 460-482. ISSN 0036-1399. doi:10.1137/0150027.

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A new bifurcation phenomenon, called complex bifurcation, is studied. The basic idea is simply that real solution paths of real analytic problems frequently have complex paths bifurcating from them. It is shown that this phenomenon occurs at fold points, at pitchfork bifurcation points, and at isola centers. It is also shown that perturbed bifurcations can yield two disjoint real solution branches that are connected by complex paths bifurcating from the perturbed solution paths. This may be useful in finding new real solutions. A discussion of how existing codes for computing real solution paths may be trivially modified to compute complex paths is included, and examples of numerically computed complex solution paths for a nonlinear two point boundary value problem, and a problem from fluid mechanics are given.

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Additional Information:© 1990 Society for Industrial and Applied Mathematics. Received March 03, 1986; Accepted May 09, 1989. This research was supported in part by United States Department of Energy contract DE-AS03-76SF-00767, and by United States Army Research Office contract DAAG29-80-C-0041.
Funding AgencyGrant Number
Department of Energy (DOE)DE-AS03-76SF-00767
Army Research Office (ARO)DAAG29-80-C-0041
Subject Keywords:bifurcation theory; nonlinear differential equations; path following
Issue or Number:2
Classification Code:AMS Subject Headings: 35B32, 34C30, 58F14, 58C28
Record Number:CaltechAUTHORS:20120424-132606071
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Official Citation:Complex Bifurcation from Real Paths M. E. Henderson and H. B. Keller, SIAM J. Appl. Math. 50, 460 (1990), DOI:10.1137/0150027
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:30287
Deposited By: Jason Perez
Deposited On:25 Apr 2012 20:32
Last Modified:09 Nov 2021 19:44

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