Abstract & Overview
As mathematical models of biological pattern generation, this study investigates the dynamics of the fractional discrete Gierer-Meinhardt reaction-diffusion system.After deriving the discrete noninteger fractional variant of the Gierer-Meinhardt system and establishing that the system has a unique equilibrium, we analyze the system's local asymptotic behavior in both the presence and absence of diffusion.The conditions for the global stability of the steady-state solution are determined using relevant approaches and the Lyapunov method.Throughout the study, two comprehensive biological models and simulations are employed to validate the utility of the considered approach.