Characterize UPOs and heteroclinic connections in the high-dimensional neuromechanical N-link model

Determine the existence, number, and structure of unstable periodic orbits and the heteroclinic trajectories connecting them to the main global stable periodic orbit in the high-dimensional Poincaré dynamics of the N-link neuromechanical undulatory locomotion model with local exteroceptive torque-load feedback, for general N and parameter regimes.

Background

Beyond the overall similarity to Purcell’s three-link case, the authors note that finer dynamical structures in the full N-link system remain unresolved due to the large number of degrees of freedom. These include how many unstable periodic orbits may exist and how they connect via heteroclinic trajectories to the stable periodic orbit.

Understanding these fine structures would complete the dynamical systems picture underlying robustness, transients, and manoeuvring strategies in the model.

References

Nonetheless, fine structures, such as the presence and number of UPOs and the corresponding trajectories connecting them to the main SPO, have not been fully analysed because of the large degrees of freedom, which are left for future work.

— Robust undulatory locomotion via neuromechanical adjustments in a dissipative medium  (2405.01802 - Ishimoto et al., 2024) in Section 6, Concluding remarks