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    Existence of wave front solutions of an integral differential equation in nonlinear nonlocal neuronal network

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    2014Existance of wave_Network.pdf (1.861Mb)
    Date
    2014
    Author
    Zhang, Lijun
    Khalique, Chaudry Masood
    Zhang, Linghai
    Yuan, Jie
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    Abstract
    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.
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    http://hdl.handle.net/10394/18181
    http://dx.doi.org/10.1155/2014/753614
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