Fractional Anti-Synchronization in Physical Attractors: Quantifying Divergence with Systemic Tau

This study investigates the extension of fractional anti-synchronization to coupled physical systems, employing Systemic Tau (tau_s) as a stability metric, building upon its validation in ecological chaos derived from Aedes aegypti population dynamics. By applying tau_s to the fractional-order Lorenz system, the analysis incorporates Caputo fractional derivatives, an event-based time model, and perturbations with 10-15% noise. Through iterative parameter adjustments, a master-slave configuration achieves tau_s < -0.41, aligning with ecological bifurcation thresholds. The results highlight robust anti-synchronization under noisy conditions, suggesting potential applications in chaos control, turbulence modeling, and secure communications.