Dual Regimes of Nonlinear Energy Dynamics in FPUT Lattices: From Recurrence to Chaos in Communication-Oriented Systems

Nonlinear oscillator networks such as the Fermi–Pasta–Ulam–Tsingou (FPUT) chain exhibit rich dynamical behavior that bridges integrable motion and chaotic energy diffusion. In this work, a comprehensive numerical and theoretical framework is developed to analyze the transition from coherent modal excitation to ergodicity, with a particular focus on its implications for signal propagation and wave-based computation. A dual decay model is introduced to characterize the critical energy threshold required for ergodic behavior, revealing distinct exponential and power-law scaling regimes as functions of the nonlinear coupling parameter. Numerical simulations further demonstrate that this threshold scales inversely with system size, highlighting the role of mode density in enabling energy delocalization. Spectral analyses reveal both reversible modal recurrences and irreversible energy cascades, while phase-space diagnostics via Poincaré sections uncover the progressive breakdown of invariant structures and the emergence of global chaos. The results provide a predictive framework for tuning energy and nonlinearity to preserve coherence or induce controlled randomness in oscillator-based communication and computing systems. The integration of dynamical systems theory with applied nonlinear modeling offers new tools for the design of robust, tunable, and scalable information technologies. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.