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Bohmer, K. and Mei, Z. (1990) On a Numerical Liapunov-Schmidt Method. In: Allgower, E.L. and Georg, K., Eds., Computational Solution of Nonlinear Systems of Equations, Lectures in Applied Mathematics, Vol. 26, 79-98.

has been cited by the following article:

• TITLE: Turing Instability of Gray-Scott Reaction-Diffusion Model with Time Delay Effects

  AUTHORS: Suqi Ma

  KEYWORDS: Reaction Diffusion, Turing Bifurcation, Normal Form, Time Delay

  JOURNAL NAME: International Journal of Modern Nonlinear Theory and Application, Vol.12 No.2, June 16, 2023

  ABSTRACT: The reaction diffusion Gray-Scott model with time delay is put forward with the assumption of Neumann boundary condition is satisfied. Based on the Turing bifurcation condition, the Turing curves on two parameter plane are discussed without time delay. The normal form is computed via applying Lyapunov-Schmidt reduction method in system of PDE, and the bifurcating direction of pitchfork bifurcation underlying codimension-1 singularity of Turing point is computed. The continuation of Pitchfork bifurcation is simulated with varying free parameter continuously near the turing point, which is in coincidence with the theoritical analysis results. The wave pattern formation in the case of turing instability is also simulated which discover Turing oscillation phenomena from periodicity to irregularity.