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Published online by Cambridge University Press: 27 September 2017
A two-dimensional sheet model for solar filaments (Kippenhahn and Schluter configuration) is considered. We investigate, the quasi-static evolution of gravito-magnetohydrostatic equlibria in exploring the response of massive current sheets to a slow continuous variation of the mass/flux ratio with fixed boundary conditions. A catastrophic behavior of the field topology is found to occur in the sequence following the formation of a cusp point (bifurcation).