The AMDCF Universal Framework: A Unified Non-Local Integro-Differential Approach for Complex Systems

For decades, scientific disciplines have been siloed, developing separate mathematical models for distinct phenomena. This paper introduces the Adaptive Memory-Driven Coupling Framework (AMDCF) as a unified theoretical paradigm capable of describing complex systems across all scales. By integrating non-local spatial interactions (topological diffusion), non-Markovian temporal memory, and non-linear safety valves, AMDCF provides a single mathematical language for chaotic, biological, and quantum systems. We demonstrate the theory's universal validity through cross-disciplinary validations, from plasma turbulence and quantum decoherence to ecological tipping points and bacterial evolution, establishing AMDCF as a new frontier in complex systems science.