LINLBF: A Program for Continuation and Bifurcation Analysis of Equilibria Up to Codimension Three

An approach which combines recent results on local bifurcation theory with the continuation method is discussed. This approach has been implemented in the LINLBF program. The program provides an advanced continuation strategy to analyze bifurcations of equilibrium points of ODEs up to codimension three singularities. We discuss the main principles, mathematics and numerics of the program, and illustrate this on a three-dimensional chemical kinetic model depending upon seven parameters. A new interactive version of the program for IBM PC compatibles is also described.