Two‐Parameter Dynamics and Spatiotemporal Patterns in a Fractional Goldbeter‐Lefever Model of Glycolysis

ABSTRACT This study investigates the dynamics of glycolytic oscillations using a time‐fractional reaction‐diffusion Goldbeter‐Lefever model with Caputo fractional derivatives. We study both the ordinary differential system (ODE) and the spatially extended system (PDE) to understand how the fractional order affects stability and pattern formation. The model extends the classical Goldbeter‐Lefever system by including memory effects through the fractional derivative. Our results show that lowering the fractional order enlarges the stability region of the steady state and changes the onset of Turing instabilities. We provide analytical conditions using linearization and spectral methods, and confirm the results with numerical simulations using a predictor‐corrector scheme and finite difference method. These results show the important role of memory and anomalous diffusion in biochemical systems. This work helps better understand how fractional dynamics affect metabolic oscillations.