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• W4220776914 abstract "Gierer–Meinhardt system is a molecularly plausible model to describe pattern formation. When gene expression time delay is added, the behavior of the Gierer–Meinhardt model profoundly changes. In this paper, we study the delayed reaction–diffusion Gierer–Meinhardt system with Neumann boundary condition. Necessary and sufficient conditions for the occurrence of Turing instability, Hopf bifurcation and Turing–Hopf bifurcation deduced by diffusion and gene expression time delay are obtained through linear stability analysis and root distribution of the characteristic equation with two transcendental terms. With the aid of the normal form Turing–Hopf bifurcation and numerical simulations, we theoretically and numerically obtain the expected solutions including stable spatially inhomogeneous steady states, stable spatially homogeneous periodic orbit and stable spatially inhomogeneous periodic orbit from Turing–Hopf bifurcation." @default.
• W4220776914 created "2022-04-03" @default.
• W4220776914 creator A5061884803 @default.
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• W4220776914 date "2022-03-30" @default.
• W4220776914 modified "2023-10-04" @default.
• W4220776914 title "Turing–Hopf Bifurcation in Diffusive Gierer–Meinhardt Model" @default.
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• W4220776914 doi "https://doi.org/10.1142/s0218127422500468" @default.
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