Using Lin's method to solve Bykov's problems
The authors extend the study of the dynamics near T-point heteroclinic cycles from 3-dimensional space, as previously investigated by Bykov, to higher dimensional space. By considering the existence of `piecewise continuous orbits' called Lin orbits, they employ a functional analytic approach to derive a set of bifurcation equations whose solutions represented orbits of a nonwandering set. In the analysis, they distinguish between cases with real and complex leading eigenvalues of the equilibria. In particular, they reveal the existence of richer dynamics when one of the leading eigenvalues is complex.
scientific article; zbMATH DE number 6332810
scientific article