A neural field models the large scale behaviour of large groups of neurons. We extend previous results for these models by including a diffusion term into the neural field, which models direct, electrical connections. We extend known and prove new sun-star calculus results for delay equations to be able to include diffusion and explicitly characterise the essential spectrum. For a certain class of connectivity functions in the neural field model, we are able to compute its spectral properties and the first Lyapunov coefficient of a Hopf bifurcation. By examining a numerical example, we find that the addition of diffusion suppresses non-synchronised steady-states while favouring synchronised oscillatory modes.

中文翻译：

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具有传输延迟和扩散的神经场模型

一个神经场模拟了大批神经元的大规模行为。我们通过将扩散项包含到神经场中来扩展这些模型的先前结果，该扩散项对直接的电气连接进行建模。我们扩展了已知的范围并证明了延迟方程的新的太阳星演算结果，能够包含扩散并明确表征基本频谱。对于神经场模型中的某类连通性函数，我们能够计算其光谱特性和Hopf分支的第一个Lyapunov系数。通过检查一个数值示例，我们发现增加扩散可以抑制非同步稳态，同时有利于同步振荡模式。