Many natural and engineered systems exhibit structured oscillatory behaviour arisingfrom the interplay of nonlinear feedback and multiple temporal scales. A fundamentalopen question is: what is the minimal architecture sufficient to generate and sustainsuch behaviour? This paper introduces the LOGOS (Layered Oscillatory Generationand Organisation System) framework, a three-layer delay-feedback dynamicalarchitecture governed by a system of coupled delay differential equations (DDEs)with hierarchical time delays and a smooth nonlinear response function. Numericalexploration reveals that the system produces stable oscillatory regimes characterisedby frequency synchronisation, circulating feedback dynamics, and slow–fast regulation,operating within a corridor of controlled oscillatory complexity rather thanconverging to equilibrium or to fully developed chaos. Parameter sweeps demonstratethat strong oscillatory behaviour emerges robustly when the delay hierarchy satisfiesτ1 : τ2 : τ3 ≈ 1 : 2–3 : 4–6 and the coordination parameter lies near Λ ≈ 0.35–0.42.These findings suggest that layered nonlinear delay feedback constitutes a minimalmechanism for generating structured rhythmic dynamics.
Mustafa Serkan Taşkoyan (Sat,) studied this question.