Nonlinear Temporal Dynamics: A New Mathematical Framework for Time as a Resonance-Based Phenomenon

This paper introduces a novel mathematical framework redefining time as a dynamic, nonlinear phenomenon, governed by local resonances and system interactions rather than a universal linear metric. The proposed model, ϕ(u), replaces the traditional temporal axis with a function that integrates past, present, and future into a continuous process. This approach bridges quantum correlations, large-scale coherence, and gravitational interactions without reliance on absolute time. Applications include quantum mechanics, cosmology, and complex system dynamics, providing a unified perspective on temporal behavior across scales.