Josef Hofbauer:

Heteroclinic Cycles in Ecological Differential Equations

Proceedings of the EQUADIFF 8 (Bratislava 1993), Tatra Mount. Math. Publ. 4 (1994), 105-116.

Abstract. Differential equations on Rn that leave certain hyperplanes invariant, arise as models in mathematical biology and in systems with symmetry. In such systems heteroclinic cycles occur in a robust way. We survey examples from the literature and propose a classification into `planar', simple, and multiple heteroclinic cycles (or heteroclinic networks). We associate a characteristic matrix to such objects, consisting of certain eigenvalues at the fixed points, and show how to read off stability properties from this matrix. Instead of Poincare sections we use average Lyapunov functions to obtain stability results.

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