Deformations of the bifurcation diagram due to discretization

Bigge, J.; Bohl, E.

doi:10.1090/S0025-5718-1985-0804931-X

Deformations of the bifurcation diagram due to discretization
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by J. Bigge and E. Bohl PDF

Math. Comp. 45 (1985), 393-403 Request permission

Abstract:

With a singular perturbation problem occurring in chemical reaction processes, substantial changes of the bifurcation diagram due to discretization are demonstrated. It is shown that a discrete system can possess any number of solutions, whereas the underlying continuous problem has exactly one solution. In addition to that, there is no way to favor one of the various discrete solutions as the one approximating the continuous solution.

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