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Bifurcation Chaos"],"published-print":{"date-parts":[[2022,3,30]]},"abstract":"<jats:p> Gierer\u2013Meinhardt system is a molecularly plausible model to describe pattern formation. When gene expression time delay is added, the behavior of the Gierer\u2013Meinhardt model profoundly changes. In this paper, we study the delayed reaction\u2013diffusion Gierer\u2013Meinhardt system with Neumann boundary condition. Necessary and sufficient conditions for the occurrence of Turing instability, Hopf bifurcation and Turing\u2013Hopf 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\u2013Hopf 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\u2013Hopf bifurcation. <\/jats:p>","DOI":"10.1142\/s0218127422500468","type":"journal-article","created":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T09:37:34Z","timestamp":1648719454000},"source":"Crossref","is-referenced-by-count":10,"title":["Turing\u2013Hopf Bifurcation in Diffusive Gierer\u2013Meinhardt Model"],"prefix":"10.1142","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7725-2538","authenticated-orcid":false,"given":"Rui","family":"Yang","sequence":"first","affiliation":[{"name":"College of Sciences, Shanghai Institute of Technology, Shanghai 201418, P. R. 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