| 边界条件下的Fizhugh Nagumo模型斑图动力学研究 |
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| 引用本文： | 郑前前,申建伟. 边界条件下的Fizhugh Nagumo模型斑图动力学研究[J]. 动力学与控制学报, 2020, 18(1): 82-87 |
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| 作者姓名： | 郑前前 申建伟 |
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| 作者单位： | 许昌学院 数学与统计学院,许昌 461000,许昌学院 数学与统计学院,许昌 461000 |
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| 基金项目： | 国家自然科学基金资助项目(11772291)、河南省青年人才托举工程和许昌学院科研项目(2020HYTP012,2020ZD012) |
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| 摘 要： | 本文主要研究边界条件下FN(FiZhUgh-Nagum)模型的神经定位动力学行为,首先针对带有扩散的FN模型进行了理论研究;然后通过离散拉普拉斯算子的方法,得到了FN模型带有边界的常微分方程;接着分析了边界条件对系统斑图形态的具体影响,对混合边界不同参数取值进行了研究,得到了混合边界值和矩阵谱倒数的关系;最后通过数值模拟的方法验证了已有实验结果,解释了上述系统的斑图机制,给出了斑图形态的调控方法。
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| 关 键 词： | FN模型 边界条件 离散 拉普拉斯算子 斑图 欧拉法 |
| 收稿时间： | 2019-08-30 |
| 修稿时间： | 2019-12-13 |
Studies on pattern dynamics of Fizhugh-Nagumo model under boundary conditions |
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| Zheng Qianqian,Shen Jianwei. Studies on pattern dynamics of Fizhugh-Nagumo model under boundary conditions[J]. Journal of Dynamics and Control, 2020, 18(1): 82-87 |
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| Authors: | Zheng Qianqian Shen Jianwei |
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| Affiliation: | (School of Mathematics and Statistics,Xuchang University,Xuchang 461000,China) |
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| Abstract: | In this paper,the neural localization dynamics behavior of FN (fizhugh nagumo) model under boundary conditions is studied.The theoretical study is carried out on the FN model with diffusion,and the normal differential equation with boundary is obtained by the method of discrete Laplace operator,then the specific effect of boundary conditions on the system is analyzed.Also,the different parameter of the mixed boundary is studied and the relationship between a mixed boundary value and matrix spectral is obtained.Finally,the results are verified by numerical simulation,the new pattern mechanism of FN model about grid cell is proposed,and the regulation method of pattern formation is present. |
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| Keywords: | FN model pattern formation Laplace operator Euler method discrete |
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