On a new version of grierer-meinhardt model using fractional discrete calculus

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 non-integer 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.