Stability of Turing bifurcation in a weighted networked reaction–diffusion system

By introducing a weighted networked structure to the classical reaction–diffusion system, we investigate the Turing bifurcation which changes the trivial equilibrium to the nontrivial equilibrium. We show the existence of Turing bifurcation if the diffusion rate is large. By a weakly nonlinear analysis, we induce the amplitude equation of Turing bifurcation. By analyzing the amplitude equation, we show that the Turing bifurcation is stable.