Integrating Critical Slowing Down (CSD) with Filtered AMDCF Control for Predictive Rescue of Ecological Tipping Points

This paper presents a mathematically rigorous ecological control strategy using the Adaptive Memory-Driven Coupling Framework (AMDCF). We model a population subjected to a shrinking carrying capacity (K) and a fixed Allee threshold (A). Crucially, we utilize the Critical Slowing Down (CSD) signal—specifically the detrended rolling variance—as an early warning indicator. When K falls below A, an "Allee Trap" condition is triggered, adding an additional mortality term to account for irreversible environmental collapse. To prevent actuator shock, an Exponential Moving Average (EMA) filter is applied to the predictive rescue force. The simulation demonstrates that the CSD-triggered AMDCF controller successfully rescues the population (final state: 344.4) while the uncontrolled system collapses (0.7). This framework provides a realistic, implementable mathematical foundation for biodiversity conservation and ecosystem resilience.