A portable bifurcation and stability analysis package, called BISTAB, is described. The package is written in FORTRAN v and can follow the connected set of equilibrium curves for a system of nonlinear ordinary differential equations in the stat$e\times parameter$ space by varying a bifurcation parameter. The curves are traced from an initial point with the continuation method of {\itM. Kubíček} [ACM Trans. Math. Software 2, 98-107 (1976; Zbl 0317.65019)], and the tangent method of {\itH. B. Keller} [Numerical solution of bifurcation and nonlinear eigenvalue problems. Applications of Bifurcation Theory, Proc. adv. Semin., Madison/Wis. 1976, 359-384 (1977)] is used to find initial points on bifurcating curves near simple bifurcation points. Linearized stability analysis, location of Hopf bifurcation points, and sorting of points for plotting are also supported. While the package contains no new numerical methods, the lack of a requirement for any derivative information higher than the Jacobian makes BISTAB computationally efficient and useful for applied problems where nonnumerical bifurcation analysis may be difficult.

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  1. Wood, Eric F.; Kempf, James A.; Mehra, Raman K.: BISTAB: A portable bifurcation and stability analysis package (1984)