Rigorous bifurcation analysis of the original non-autonomous periodically driven systems

Conduct a rigorous bifurcation analysis of the non-autonomous extended Stuart–Landau oscillator subjected to additive periodic forcing and multiplicative periodic forcing with linear and quadratic feedback, to characterize the anticipated complex dynamics including quasi-periodic solutions and chaos.

Background

The paper analyzes averaged autonomous reductions of the periodically driven extended Stuart–Landau oscillator and finds diverse bifurcation structures. The authors expect the full non-autonomous systems to exhibit even richer dynamics.

They explicitly highlight the challenge of performing rigorous bifurcation analyses directly on the original non-autonomous formulations with additive and multiplicative forcing, anticipating quasi-periodic and chaotic behavior.

References

Several open questions remain to be examined. Third, as we have mentioned above, the original nou-autonomous systems esl_p, esl_mp, and esl_mp2 are expected to have complex and diverse dynamics, including quasi-periodic solutions and chaos. Bifurcation analyses of these systems would be challenging.

— Periodic forces combined with feedback induce quenching in a bistable oscillator (2405.19929 - Kato et al., 30 May 2024) in Section 6 (Discussion), paragraph beginning “Several open questions remain to be examined.”, Third item