On a New Version of Grierer-Meinhardt Model Using Fractional Discrete Calculus
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Abstract
As mathematical models of biological pattern generation, this study studies the dynamics of 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 with both the presence and absence of the diffusion. The requirements for the steady-state solution’s global stability are found with the help of relevant approaches and the Lyapunov method. Throughout the study, two large biological models and simulations are employed to validate the usefulness of the considered approach.
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