Periodic Forcing of a Heteroclinic Network

We present a comprehensive mechanism for the emergence of rotational horseshoes and strange attractors in class two-parameter families periodically-perturbed differential equations defining flow on three-dimensional manifold. When both parameters are zero, its exhibits an attracting heteroclinic network associated to two periodic solutions. After slightly increasing parameters, while keeping two-dimensional connection unaltered, we focus our attention case where invariant manifolds solutions do not intersect. prove wide range dynamical behaviour, ranging from quasi-periodic torus Hénon-like attractors. illustrate results with explicit example.