Pakdaman K, Malta C P, Grotta-Ragazzo C, Vibert J F
INSERM V444 ISARS Faculté de Médecine Saint-Antoine, Paris, France.
Neural Comput. 1997 Feb 15;9(2):319-36. doi: 10.1162/neco.1997.9.2.319.
Little attention has been paid in the past to the effects of interunit transmission delays (representing axonal and synaptic delays) on the boundary of the basin of attraction of stable equilibrium points in neural networks. As a first step toward a better understanding of the influence of delay, we study the dynamics of a single graded-response neuron with a delayed excitatory self-connection. The behavior of this system is representative of that of a family of networks composed of graded-response neurons in which most trajectories converge to stable equilibrium points for any delay value. It is shown that changing the delay modifies the "location" of the boundary of the basin of attraction of the stable equilibrium points without affecting the stability of the equilibria. The dynamics of trajectories on the boundary are also delay dependent and influence the transient regime of trajectories within the adjacent basins. Our results suggest that when dealing with networks with delay, it is important to study not only the effect of the delay on the asymptotic convergence of the system but also on the boundary of the basins of attraction of the equilibria.
过去，人们很少关注单元间传输延迟（代表轴突和突触延迟）对神经网络中稳定平衡点吸引域边界的影响。作为更好地理解延迟影响的第一步，我们研究了具有延迟兴奋性自连接的单个分级响应神经元的动力学。该系统的行为代表了由分级响应神经元组成的一类网络的行为，其中对于任何延迟值，大多数轨迹都收敛到稳定平衡点。结果表明，改变延迟会改变稳定平衡点吸引域边界的“位置”，而不会影响平衡点的稳定性。边界上轨迹的动力学也与延迟有关，并影响相邻吸引域内轨迹的暂态。我们的结果表明，在处理具有延迟的网络时，不仅要研究延迟对系统渐近收敛的影响，还要研究其对平衡点吸引域边界的影响，这一点很重要。
