Turing–Hopf bifurcation and spatiotemporal patterns in a Gierer–Meinhardt system with gene expression delay
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| Format: | Artículo científico |
| Langue: | en |
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Vilniaus Universitetas
2021
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| _version_ | 1876425351126581248 |
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| author | Zhao Shuangrui |
| author_facet | Zhao Shuangrui |
| contents | Turing–Hopf bifurcation and spatiotemporal patterns in a Gierer–Meinhardt system with gene expression delay Zhao Shuangrui Wang Hongbin Jiang Weihua Matemáticas delay Gierer Turing normal form spatiotempo In this paper, we consider the dynamics of delayed Gierer–Meinhardt system, which is used as a classic example to explain the mechanism of pattern formation. The conditions for the occurrence of Turing, Hopf and Turing–Hopf bifurcation are established by analyzing the characteristic equation. For Turing–Hopf bifurcation, we derive the truncated third-order normal form based on the work of Jiang et al. 11, which is topologically equivalent to the original equation, and theoretically reveal system exhibits abundant spatial, temporal and spatiotemporal patterns, such as semistable spatially inhomogeneous periodic solutions, as well as tristable patterns of a pair of spatially inhomogeneous steady states and a spatially homogeneous periodic solution coexisting. Especially, we theoretically explain the phenomenon that time delay inhibits the formation of heterogeneous steady patterns, found by S. Lee, E. Gaffney and N. Monk The influence of gene expression time delays on Gierer–Meinhardt pattern formation systems, Bull. Math. Biol., 72(8):2139–2160, 2010. 2021 artículo científico 1392-5113 https://www.redalyc.org/articulo.oa?id=694172973005 https://www.redalyc.org/journal/6941/694172973005/ https://www.redalyc.org/journal/6941/694172973005/html/ https://www.redalyc.org/journal/6941/694172973005/694172973005.epub https://www.redalyc.org/journal/6941/694172973005/movil en http://www.redalyc.org/revista.oa?id=6941 Nonlinear Analysis: Modelling and Control application/pdf Vilniaus Universitetas Nonlinear Analysis: Modelling and Control (Lituania) Num.3 Vol.26 |
| format | Artículo científico |
| id | redalyc_694172973005 |
| institution | Redalyc |
| language | en |
| publishDate | 2021 |
| publisher | Vilniaus Universitetas |
| spellingShingle | Turing–Hopf bifurcation and spatiotemporal patterns in a Gierer–Meinhardt system with gene expression delay Zhao Shuangrui Matemáticas delay Gierer Turing normal form spatiotempo Turing–Hopf bifurcation and spatiotemporal patterns in a Gierer–Meinhardt system with gene expression delay Zhao Shuangrui Wang Hongbin Jiang Weihua Matemáticas delay Gierer Turing normal form spatiotempo In this paper, we consider the dynamics of delayed Gierer–Meinhardt system, which is used as a classic example to explain the mechanism of pattern formation. The conditions for the occurrence of Turing, Hopf and Turing–Hopf bifurcation are established by analyzing the characteristic equation. For Turing–Hopf bifurcation, we derive the truncated third-order normal form based on the work of Jiang et al. 11, which is topologically equivalent to the original equation, and theoretically reveal system exhibits abundant spatial, temporal and spatiotemporal patterns, such as semistable spatially inhomogeneous periodic solutions, as well as tristable patterns of a pair of spatially inhomogeneous steady states and a spatially homogeneous periodic solution coexisting. Especially, we theoretically explain the phenomenon that time delay inhibits the formation of heterogeneous steady patterns, found by S. Lee, E. Gaffney and N. Monk The influence of gene expression time delays on Gierer–Meinhardt pattern formation systems, Bull. Math. Biol., 72(8):2139–2160, 2010. 2021 artículo científico 1392-5113 https://www.redalyc.org/articulo.oa?id=694172973005 https://www.redalyc.org/journal/6941/694172973005/ https://www.redalyc.org/journal/6941/694172973005/html/ https://www.redalyc.org/journal/6941/694172973005/694172973005.epub https://www.redalyc.org/journal/6941/694172973005/movil en http://www.redalyc.org/revista.oa?id=6941 Nonlinear Analysis: Modelling and Control application/pdf Vilniaus Universitetas Nonlinear Analysis: Modelling and Control (Lituania) Num.3 Vol.26 |
| title | Turing–Hopf bifurcation and spatiotemporal patterns in a Gierer–Meinhardt system with gene expression delay |
| topic | Matemáticas delay Gierer Turing normal form spatiotempo |
| url | https://www.redalyc.org/articulo.oa?id=694172973005 https://www.redalyc.org/journal/6941/694172973005/ https://www.redalyc.org/journal/6941/694172973005/html/ https://www.redalyc.org/journal/6941/694172973005/694172973005.epub https://www.redalyc.org/journal/6941/694172973005/movil |