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This work investigates the dynamics of discrete reaction-diffusion Gierer-Meinhardt system as mathematical models of biological pattern formation. We study the system's local asymptotic behaviour with and without the diffusion once developing the discrete integer variant of the well-known Gierer-Meinhardt model and proving that the model has a unique equilibrium. The requirements for the steady-state solution's local and global stability are found with the help of relevant approaches and the Lyapunov technique. Two large biological models and simulations are used throughout the work to validate the utility of the suggested technique.
Almatroud et al. (Tue,) studied this question.