Abstract
The coordination of neural oscillations across distinct frequency bands is a fundamental mechanism of cognitive processing, with theta-gamma coupling (TGC) serving as a primary substrate for memory encoding, spatial navigation, and attentional selection. While empirical observations have long established the presence of cross-frequency coupling (CFC), the precise dynamical constraints governing its stability and efficiency remain poorly defined. This paper proposes that TGC operates at a Critical Damping Threshold, a universal resonance principle derived from the intersection of control theory, information geometry, and the Universal Spectral Decay Theorem (USDT). We demonstrate that the optimal coupling strength between theta (4–8 Hz) and gamma (30–100 Hz) oscillations corresponds to a damping ratio ζ≈0.618, the inverse of the Golden Ratio (ϕ^(−1)). This value represents the boundary between underdamped oscillatory instability and overdamped informational stagnation, maximizing the spectral quality factor Q while minimizing metabolic cost. By modeling the hippocampal formation as a non-linear feedback control system, we derive the conditions under which TGC achieves maximal information throughput. We further generalize this principle to engineering control systems and ecological networks, demonstrating that the ϕ^(−1) threshold is a universal attractor for complex adaptive systems operating at the edge of chaos. Our findings provide a unified theoretical framework for understanding cross-frequency coupling, offering novel predictions for neurophysiological experiments and robust design principles for artificial intelligence and resilient infrastructure.
