Determining Critical Temperature Differences of Low-Temperature-Differential Stirling Engines: Nonlinear Dynamics Approach

What the math gives to ML

The paper provides a constructive homoclinic-bifurcation criterion for the disappearance of sustained rotation in a delayed, damped nonlinear oscillator. Its transferable asset is the Melnikov balance: a critical forcing amplitude is obtained when energy injected along the unperturbed homoclinic orbit exactly equals dissipative loss. This can be transferred to momentum-based neural optimization on periodic or strongly nonconvex loss landscapes, where learning-rate or gradient modulation can be tuned relative to a separatrix rather than by empirical schedules. The strongest test is a predicted sharp transition between trapped and basin-crossing optimizer trajectories at the Melnikov amplitude.