| Abstract | Concepts from linear algebra and algebraic geometry (polynomial rings) can be used to determine analytically the stationary solutions in systems of ordinary differential equations of polynomial form. The stability analysis via the Jacobian matrix often leads to complicated expressions which can hardly be analyzed. It is shown that these expressions can be simplified using elimination theory, i.e. forming quotient rings of the corresponding polynomial ring. The normal forms obtained by generating the quotient rings are representatives of the coefficients of the characteristic equation so that their sign changes in dependence of a parameter and hence the stability and local bifurcations can be determined. The procedure is illustrated using a simple surface reaction. This is a joint work with Sonja Sauerbrei. |
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