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In this paper, we investigate pattern dynamics with multivariable by using the method of matrix analysis and obtain a condition under which the system loses stability and Turing bifurcation occurs. In addition, we also derive the amplitude equation with multivariable. This is an effective tool to investigate multivariate pattern dynamics. The example and simulation used in this paper validate our theoretical results. The method presented is a novel approach to the investigation of specific real systems based on the model developed in this paper.

Turing Instability and Amplitude Equation of Reaction-Diffusion System with Multivariable