Dynamics analysis of a chemical reaction–diffusion model subject to Degn–Harrison reaction scheme
A chemical reaction–diffusion model with Degn–Harrison reaction scheme and subject to homogeneous Neumann boundary condition is revisited in this article. Local asymptotic stability, Turing instability and existence of Hopf bifurcation for the only constant positive equilibrium solution are establis...
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| Published in | Nonlinear analysis: real world applications Vol. 48; pp. 161 - 181 |
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| Format | Journal Article |
| Language | English |
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Elsevier Ltd
01.08.2019
Elsevier BV |
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| ISSN | 1468-1218 1878-5719 |
| DOI | 10.1016/j.nonrwa.2019.01.005 |
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| Abstract | A chemical reaction–diffusion model with Degn–Harrison reaction scheme and subject to homogeneous Neumann boundary condition is revisited in this article. Local asymptotic stability, Turing instability and existence of Hopf bifurcation for the only constant positive equilibrium solution are established by analyzing the relevant eigenvalue problem. In particular, a simplified explicit formula determining the properties of spatially homogeneous Hopf bifurcation is derived by employing the normal form method and the center manifold theorem for reaction–diffusion equations. Our formula here simplifies the existing one obtained in Dong et al. (2017). Numerical approximations are also carried out in order to check our theoretical predictions. |
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| AbstractList | A chemical reaction–diffusion model with Degn–Harrison reaction scheme and subject to homogeneous Neumann boundary condition is revisited in this article. Local asymptotic stability, Turing instability and existence of Hopf bifurcation for the only constant positive equilibrium solution are established by analyzing the relevant eigenvalue problem. In particular, a simplified explicit formula determining the properties of spatially homogeneous Hopf bifurcation is derived by employing the normal form method and the center manifold theorem for reaction–diffusion equations. Our formula here simplifies the existing one obtained in Dong et al. (2017). Numerical approximations are also carried out in order to check our theoretical predictions. A chemical reaction–diffusion model with Degn–Harrison reaction scheme and subject to homogeneous Neumann boundary condition is revisited in this article. Local asymptotic stability, Turing instability and existence of Hopf bifurcation for the only constant positive equilibrium solution are established by analyzing the relevant eigenvalue problem. In particular, a simplified explicit formula determining the properties of spatially homogeneous Hopf bifurcation is derived by employing the normal form method and the center manifold theorem for reaction–diffusion equations. Our formula here simplifies the existing one obtained in Dong et al. (2017). Numerical approximations are also carried out in order to check our theoretical predictions. |
| Author | Yan, Xiang-Ping Chen, Jian-Ye Zhang, Cun-Hua |
| Author_xml | – sequence: 1 givenname: Xiang-Ping surname: Yan fullname: Yan, Xiang-Ping email: xpyan72@163.com – sequence: 2 givenname: Jian-Ye surname: Chen fullname: Chen, Jian-Ye – sequence: 3 givenname: Cun-Hua surname: Zhang fullname: Zhang, Cun-Hua |
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| Keywords | Degn–Harrison reaction scheme Hopf bifurcation Local asymptotic stability Turing instability Time-periodic pattern Reaction–diffusion chemical model |
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| SubjectTerms | Boundary conditions Chemical reactions Degn–Harrison reaction scheme Diffusion Eigenvalues Hopf bifurcation Local asymptotic stability Mathematical models Organic chemistry Reaction-diffusion equations Reaction–diffusion chemical model Stability Time-periodic pattern Turing instability |
| Title | Dynamics analysis of a chemical reaction–diffusion model subject to Degn–Harrison reaction scheme |
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