Patterns of sustained oscillations in neural networks with delayed interactions

摘要

We study the Cohen-Grossberg-Hopfield model of neural networks with delayed interactions when the interconnection matrix has only real and purely imaginary eigenvalues. Two indices, the symmetry index and the antisymmetry index, are introduced and are used to describe the pattern of sustained oscillations caused by the delay. It is shown that the parameter plane of these indices is divided into two regions by a smooth curve across which the patterns of oscillations switch. It is also shown that the stability of sustained oscillations is completely determined by the third-order term of the input-output relation.