Analysis of multiple quasi-periodic orbits in recurrent neural networks

In this paper we consider a recurrent neural network model consisting of two neurons and analyze its stability using the associated characteristic model. In order to analyze the multiple quasi-periodic orbits, the strong resonance of this system, in particular that known as the R-2 bifurcation, is also studied. In the case of two neurons, one necessary condition that yields the bifurcation is found. In addition, the direction of the R-2 bifurcation is determined by applying normal form theory and the center manifold theorem. The simple conditions for ensuring the existence of multiple quasi-periodic orbits are given. The strong resonance phenomenon is analyzed using numerical simulations and is related with the codimension-two bifurcation of the high-iteration map. (C) 2015 Elsevier B.V. All rights reserved.