Extend averaging analysis to m:n synchronization regimes

Extend the averaging analysis beyond 1:1 synchronization to treat m:n frequency locking (for integers m and n) between the extended Stuart–Landau bistable oscillator and an external periodic force, in order to characterize amplitude responses and bifurcation structures in these m:n synchronized regimes.

Background

The paper develops an averaging approach focused on 1:1 synchronization to analyze amplitude response and bifurcations in an extended Stuart–Landau bistable oscillator under periodic forcing. While this yields insight into quenching and various bifurcations, the authors observe additional m:n synchronization states across the studied perturbations (see Appendix).

They explicitly note that m:n regimes were not analyzed and identify the need to expand the averaging methodology to cover these synchronization ratios, which would deepen understanding of periodically driven bistable oscillators.

References

Several open questions remain to be examined. First, Fig. \ref{reso_esl_all} in Appendix \ref{app_sync} suggests the existence of $m:n$ synchronization, which we do not focus on in this study. Expanding our averaging analysis for the $m:n$ synchronization is an important task that helps further clarify the dynamics of periodically driven bistable oscillators.

— 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.”, First item