Heteroclinic cycles in ecological differential equations

Rok, strany: 1994, 105 - 116

Differential equations on $\Bbb Rⁿ$ 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 Poincaré sections we use average Lyapunov functions to obtain stability results.

ISO 690:

Hofbauer, J. 1994. Heteroclinic cycles in ecological differential equations. In Tatra Mountains Mathematical Publications, vol. 4, no.1, pp. 105-116. 1210-3195.

APA:

Hofbauer, J. (1994). Heteroclinic cycles in ecological differential equations. Tatra Mountains Mathematical Publications, 4(1), 105-116. 1210-3195.