Influence of fractional order on the dynamic behavior of a cross-reaction diffusion model

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Abstract

This paper investigates influence of fractional order on the dynamic behavior of a cross- reaction diffusion model. Stability analysis determines the existence conditions of equilibrium points, and bifurcation analyses are performed. A numerical method combining high-order time-precision generating functions and a nine-point difference spatial discretization scheme is proposed, incorporating the short memory principle to improve computational efficiency. Numerical simulations demonstrate the spatial pattern formation of the system at different parameters, validating the effectiveness of the theoretical results. Some novel patterns are shown.

Keywords

a numerical method / stability analysis / bifurcation analysis / novel pattern / cross-reaction diffusion model

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