Lefebvre Jérémie, Longtin André, LeBlanc Victor G
Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario, Canada.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 1):041912. doi: 10.1103/PhysRevE.80.041912. Epub 2009 Oct 9.
A globally coupled network of ON and OFF cells is studied using neural field theory. ON cells increase their activity when the amplitude of an external stimulus increases, while OFF cells do the opposite given the same stimulus. Theory predicts that, without input, multiple transitions to oscillations can occur depending on feedback delay and the difference between ON and OFF resting states. Static spatial stimuli can induce or suppress global oscillations via a Andronov-Hopf bifurcation. This is the case for either polarity of such stimuli. In contrast, only excitatory inputs can induce or suppress oscillations in an equivalent network built of ON cells only even though oscillations are more prevalent in such systems. Nonmonotonic responses to local stimuli occur where responses lateral to the stimulus switch from excitatory to inhibitory as the input amplitude increases. With local time-periodic forcing, the unforced cells oscillate at twice the driving frequency via full-wave rectification mediated by the feedback. Our results agree with simulations of the neural field model, and further, qualitative agreement is found with the behavior of a network of spiking stochastic integrate-and-fire model neurons.
使用神经场理论研究了由开细胞和关细胞组成的全局耦合网络。当外部刺激的幅度增加时，开细胞会增加其活动，而在相同刺激下，关细胞的情况则相反。理论预测，在没有输入的情况下，根据反馈延迟以及开细胞和关细胞静息状态之间的差异，可能会发生多次向振荡的转变。静态空间刺激可以通过安德罗诺夫 - 霍普夫分岔诱导或抑制全局振荡。对于此类刺激的任何极性都是如此。相比之下，在仅由开细胞构建的等效网络中，只有兴奋性输入才能诱导或抑制振荡，尽管振荡在这类系统中更为普遍。当刺激横向的响应随着输入幅度的增加从兴奋性转变为抑制性时，会出现对局部刺激的非单调响应。在局部时间周期强迫下，未受强迫的细胞通过反馈介导的全波整流以驱动频率的两倍振荡。我们的结果与神经场模型的模拟结果一致，此外，还发现与脉冲随机积分发放模型神经元网络的行为存在定性一致性。
