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Delay Reaction-Diffusion Systems via Discrete Dynamics
SIAM Journal on Mathematical Analysis ( IF 2.2 ) Pub Date : 2020-12-17 , DOI: 10.1137/19m1304477 Alfonso Ruiz-Herrera
SIAM Journal on Mathematical Analysis ( IF 2.2 ) Pub Date : 2020-12-17 , DOI: 10.1137/19m1304477 Alfonso Ruiz-Herrera
SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 6297-6312, January 2020.
In this paper, we analyze a class of reaction-diffusion systems with delay and a Neumann condition from the dynamical behavior of the map that determines the equilibria. For scalar equations, a similar analysis was given by Yi and Zou in [Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 466 (2010), pp. 2955--2973]. There are strong differences between the scalar equations and the systems. We show with an example that the direct extension of the results by Yi and Zou in [Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 466 (2010), pp. 2955--2973] to systems is not possible. This forces us to introduce additional assumptions. However, our approach is sufficiently general to be applicable to a wide variety of models, including neural networks and population dynamics. In some cases, our technique gives the optimal conditions for the global attraction.
中文翻译：
通过离散动力学延迟反应扩散系统
SIAM数学分析杂志，第52卷，第6期，第6297-6312页，2020年1月。
在本文中，我们从确定平衡的图的动力学行为中分析了一类具有时滞和诺伊曼条件的反应扩散系统。对于标量方程，Yi和Zou在[Proc。R. Soc。nd 老师 数学。物理 。Sci。，466（2010），pp。2955--2973]。标量方程和系统之间存在很大差异。我们以一个例子说明，在[Proc。R. Soc。nd 老师 数学。物理 。Sci。，466（2010），pp。2955--2973]无法应用于系统。这迫使我们引入其他假设。但是，我们的方法具有足够的通用性，可适用于多种模型，包括神经网络和种群动态。在某些情况下，
更新日期：2020-12-18
In this paper, we analyze a class of reaction-diffusion systems with delay and a Neumann condition from the dynamical behavior of the map that determines the equilibria. For scalar equations, a similar analysis was given by Yi and Zou in [Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 466 (2010), pp. 2955--2973]. There are strong differences between the scalar equations and the systems. We show with an example that the direct extension of the results by Yi and Zou in [Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 466 (2010), pp. 2955--2973] to systems is not possible. This forces us to introduce additional assumptions. However, our approach is sufficiently general to be applicable to a wide variety of models, including neural networks and population dynamics. In some cases, our technique gives the optimal conditions for the global attraction.
中文翻译：
通过离散动力学延迟反应扩散系统
SIAM数学分析杂志，第52卷，第6期，第6297-6312页，2020年1月。
在本文中，我们从确定平衡的图的动力学行为中分析了一类具有时滞和诺伊曼条件的反应扩散系统。对于标量方程，Yi和Zou在[Proc。R. Soc。nd 老师 数学。物理 。Sci。，466（2010），pp。2955--2973]。标量方程和系统之间存在很大差异。我们以一个例子说明，在[Proc。R. Soc。nd 老师 数学。物理 。Sci。，466（2010），pp。2955--2973]无法应用于系统。这迫使我们引入其他假设。但是，我们的方法具有足够的通用性，可适用于多种模型，包括神经网络和种群动态。在某些情况下，
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