Turing Instability and Turing–Hopf Bifurcation in Diffusive Schnakenberg Systems with Gene Expression Time Delay

  title={Turing Instability and Turing–Hopf Bifurcation in Diffusive Schnakenberg Systems with Gene Expression Time Delay},
  author={Weihua Jiang and Hongbin Wang and Xun Cao},
  journal={Journal of Dynamics and Differential Equations},
In this paper, we study the delayed reaction–diffusion Schnakenberg systems with Neumann boundary conditions. Sufficient and necessary conditions for the occurrence of Turing instability are obtained, and the existence of Turing, Hopf and Turing–Hopf bifurcation for the model are also established. Furthermore, for Turing–Hopf bifurcation, the explicit formula of the truncated normal form up to third order is derived. With the aid of these formulas, we determine the regions on two parameters… 

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