Bifurcations of periodic and antiperiodic orbits near an equilibrium in autonomous differential delay systems with one or two delays

What the math gives to ML

The paper studies variational bifurcations of periodic and antiperiodic solutions near the zero equilibrium in autonomous differential-delay systems whose vector field is the gradient of an even potential. Its transferable mechanism is a computable resonance condition: delay-induced Fourier modes become nontrivial when the Hessian of the potential matches the complex characteristic multiplier associated with the imposed antiperiodic period. This can be brought into recurrent or state-space neural networks as a spectral bifurcation monitor and as an optional periodic-attractor regularizer, with experiments testing whether predicted resonance frequencies coincide with the emergence of oscillatory hidden-state trajectories.