Concrete example with an f.a.s. aperiodic sequence

Construct an explicit dynamical system that admits a heteroclinic or homoclinic network together with a fragmentarily asymptotically stable aperiodic sequence of connections.

Background

Although the paper develops a framework for stability of sequences and discusses examples suggesting or obstructing aperiodic behavior, a fully worked dynamical system exhibiting an f.a.s. aperiodic sequence is not presently available.

Such an example would validate the theoretical framework, provide test cases for proposed criteria, and clarify the extent to which aperiodicity can accompany positive-measure attraction to networks.