Existence of Wave Front Solutions of an Integral Differential Equation in Nonlinear Nonlocal Neuronal Network
An integral-differential model equation arising from neuronal networks with very general kernel functions is considered in this paper. The kernel functions we study here include pure excitations, lateral inhibition, lateral excitations, and more general synaptic couplings (e.g., oscillating kernel f...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/753614 |
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| _version_ | 1832555097669763072 |
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| author | Lijun Zhang Linghai Zhang Jie Yuan C. M. Khalique |
| author_facet | Lijun Zhang Linghai Zhang Jie Yuan C. M. Khalique |
| author_sort | Lijun Zhang |
| collection | DOAJ |
| description | An integral-differential model equation arising from neuronal networks with very general kernel functions is considered in this paper. The kernel functions we study here include pure excitations, lateral inhibition, lateral excitations, and more general synaptic couplings (e.g., oscillating kernel functions). The main goal of this paper is to prove the existence and uniqueness of the traveling wave front solutions. The main idea we apply here is to reduce the nonlinear integral-differential equation into a solvable differential equation and test whether the solution we get is really a wave front solution of the model equation. |
| format | Article |
| id | doaj-art-27918efa36cc44b58f0f85397fb8042b |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-27918efa36cc44b58f0f85397fb8042b2025-02-03T05:49:31ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/753614753614Existence of Wave Front Solutions of an Integral Differential Equation in Nonlinear Nonlocal Neuronal NetworkLijun Zhang0Linghai Zhang1Jie Yuan2C. M. Khalique3Department of Mathematics, School of Science, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, ChinaDepartment of Mathematics, Lehigh University, 14 E Packer Avenue, Bethlehem, PA 18015, USADepartment of Mathematics, Lehigh University, 14 E Packer Avenue, Bethlehem, PA 18015, USADepartment of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical Modelling, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South AfricaAn integral-differential model equation arising from neuronal networks with very general kernel functions is considered in this paper. The kernel functions we study here include pure excitations, lateral inhibition, lateral excitations, and more general synaptic couplings (e.g., oscillating kernel functions). The main goal of this paper is to prove the existence and uniqueness of the traveling wave front solutions. The main idea we apply here is to reduce the nonlinear integral-differential equation into a solvable differential equation and test whether the solution we get is really a wave front solution of the model equation.http://dx.doi.org/10.1155/2014/753614 |
| spellingShingle | Lijun Zhang Linghai Zhang Jie Yuan C. M. Khalique Existence of Wave Front Solutions of an Integral Differential Equation in Nonlinear Nonlocal Neuronal Network Abstract and Applied Analysis |
| title | Existence of Wave Front Solutions of an Integral Differential Equation in Nonlinear Nonlocal Neuronal Network |
| title_full | Existence of Wave Front Solutions of an Integral Differential Equation in Nonlinear Nonlocal Neuronal Network |
| title_fullStr | Existence of Wave Front Solutions of an Integral Differential Equation in Nonlinear Nonlocal Neuronal Network |
| title_full_unstemmed | Existence of Wave Front Solutions of an Integral Differential Equation in Nonlinear Nonlocal Neuronal Network |
| title_short | Existence of Wave Front Solutions of an Integral Differential Equation in Nonlinear Nonlocal Neuronal Network |
| title_sort | existence of wave front solutions of an integral differential equation in nonlinear nonlocal neuronal network |
| url | http://dx.doi.org/10.1155/2014/753614 |
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