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Published April 1990 | Published
Journal Article Open

Complex Bifurcation from Real Paths


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.

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.

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