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 R^{n} 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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reprint from https://eudml.org/doc/220311