一类中立型二维神经网络模型的振动性

Oscillation of a class of 2-dimensional neutral neural network model

在无自反馈的时滞神经网络模型中加入中立行为,得到一类无自反馈的中立型二维时滞神经网络。从方程平衡解的唯一性、不稳定性以及全局有界性三个方面加以研究,结合Chafee的极限环定理,给出该系统的解的振动性的存在性条件,在一定程度上揭示了该中立型神经网络模型的更为丰富的动力学行为。数值模拟验证了结论的正确性。

By adding neutral behavior into the neural network model with delay, a kind of 2-dimensional neutral neural network model without self-feedback is obtained. The uniqueness, instability and global boundedness of equilibrium solution are investigated. By using Chafee＇ s criterion, the existence of oscillation of solutions is obtained and rich dynamical behavior is revealed. Finally, numerical simulations are performed to support the analytic resuits.