Predictive-Protective Stabilization of Pitchfork Bifurcations: A Numerical Study using the Unified AMDCF Kernel

Complex systems approaching a catastrophic regime shift (tipping point) exhibit a phenomenon known as "Critical Slowing Down" (CSD), characterized by a significant spike in local variance. In this paper, we propose a novel Predictive-Protective Framework based on the unified AMDCF (Adaptive Memory-Driven Coupling Framework) to actively suppress this instability. Using a 1D stochastic pitchfork bifurcation model as a testbed, we demonstrate that the AMDCF kernel utilizes the CSD variance spike as an early-warning predictive signal. By dynamically triggering a gain controller and incorporating a non-Markovian memory feedback, the AMDCF controller successfully protects the system from collapsing (final state: 0.3700). In contrast, the uncontrolled system undergoes a catastrophic regime shift to zero (final state: -0.0543). This work highlights the potential of the AMDCF kernel as a robust predictive control algorithm for preventing catastrophic shifts in nonlinear dynamical systems, bridging the gap between early-warning signal processing and active control engineering