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Oscillatory and Stationary Patterns in a Diffusive Model with Delay Effect
International Journal of Bifurcation and Chaos ( IF 2.2 ) Pub Date : 2021-03-20 , DOI: 10.1142/s0218127421500358
Shangjiang Guo 1 , Shangzhi Li 1 , Bounsanong Sounvoravong 2
Affiliation  

In this paper, a reaction–diffusion model with delay effect and Dirichlet boundary condition is considered. Firstly, the existence, multiplicity, and patterns of spatially nonhomogeneous steady-state solution are obtained by using the Lyapunov–Schmidt reduction. Secondly, by means of space decomposition, we subtly discuss the distribution of eigenvalues of the infinitesimal generator associated with the linearized system at a spatially nonhomogeneous synchronous steady-state solution, and then we derive some sufficient conditions to ensure that the nontrivial synchronous steady-state solution is asymptotically stable. By using the symmetric bifurcation theory of differential equations together with the representation theory of standard dihedral groups, we not only investigate the effect of time delay on the pattern formation, but also obtain some important results on the spontaneous bifurcation of multiple branches of nonlinear wave solutions and their spatiotemporal patterns.

中文翻译:

具有延迟效应的扩散模型中的振荡和平稳模式

在本文中,考虑了具有延迟效应和狄利克雷边界条件的反应-扩散模型。首先,利用Lyapunov-Schmidt约简得到空间非齐次稳态解的存在性、多重性和模式。其次,通过空间分解,我们巧妙地讨论了与线性化系统相关的无穷小生成元在空间非齐次同步稳态解下的特征值分布,进而推导了一些保证非平凡同步稳态的充分条件。解是渐近稳定的。利用微分方程的对称分岔理论和标准二面体群的表示理论,我们不仅研究了时间延​​迟对模式形成的影响,
更新日期:2021-03-20
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