Backward-time asymptotics for sequences approaching networks

Ascertain the asymptotic behavior under time reversal for trajectories that approach heteroclinic or homoclinic networks along a given sequence, and determine how backward-time dynamics relate to the network and to higher-depth heteroclinic connections.

Background

The authors’ stability notion concerns forward-time convergence to networks along sequences. They ask about the complementary backward-time dynamics, including the relationship to heteroclinic connections of higher depth.

Understanding backward-time behavior would provide a more complete dynamical picture and inform questions about bi-directional convergence and sequence concatenation.