Spiralling dynamics near heteroclinic networks

摘要: Abstract There are few explicit examples in the literature of vector fields exhibiting complex dynamics that may be proved analytically. We construct explicitly a two parameter family on three-dimensional sphere S 3 , whose flow has spiralling attractor containing following: hyperbolic equilibria, heteroclinic trajectories connecting them transversely and non-trivial hyperbolic, invariant transitive set. The set unfolds network between symmetric saddle-foci contains sequence topological horseshoes semiconjugate to full shifts over an alphabet with more symbols, coexisting Newhouse phenomena. field is restriction polynomial R 4 . In this article, we also identify global bifurcations induce chaotic different types.