两类双阈值二元神经网络模型的渐近行为

Asymptotic Behaviors of Solutions of Two Types of Neural Networks with Two Thresholds

考虑两类双阈值二元神经网络模型,研究了具变号型初值解的渐近行为。结果表明:对大阈值情形,模型有唯一平衡点;对临界阈值情形,模型有两个或三个平衡点。进一步,在临界阈值情形,对时滞τ、阈值σ及初值Φ建立了保证系统趋于不同平衡点之一的充要条件。这些结论对相关文献作了较大推广。

Concentrating on the case where φ-σ and ψ-σ have sign changes on [-τ, 0],two types of models of neural networks with two thresholds and two neurons are considered. It＇s found that every solution （x^Ф（t） ,y^Ф（t） ） （Ф= （φ,ψ） is initial value） single equilibrium if the absolute values of threshold values are large. In particular, some necessary and sufficient conditions are established, in terms of r and Ф, which guarantee （x^Ф（t）,y^Ф（t）） tends to those equilibria respectively in the critical case.