Spek Len, Kuznetsov Yuri A, van Gils Stephan A
Department of Applied Mathematics, University of Twente, Enschede, The Netherlands.
Department of Mathematics, Utrecht University, Utrecht, The Netherlands.
J Math Neurosci. 2020 Dec 9;10(1):21. doi: 10.1186/s13408-020-00098-5.
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.
神经场对大量神经元的大规模行为进行建模。我们通过在神经场中纳入一个扩散项来扩展这些模型的先前结果，该扩散项对直接的电连接进行建模。我们扩展了已知的关于延迟方程的太阳 - 星演算结果并证明了新的结果，以便能够纳入扩散并明确表征本质谱。对于神经场模型中的某一类连接函数，我们能够计算其谱性质以及霍普夫分岔的第一个李雅普诺夫系数。通过研究一个数值例子，我们发现扩散的加入抑制了非同步稳态，同时有利于同步振荡模式。
