Convergence in Networks With Counterclockwise Neural Dynamics

The notion of counterclockwise (ccw) input-output (I-O) dynamics, introduced by Angeli (2006) to deal with questions of multistability in interconnected dynamical systems, is applied and further developed in order to analyze convergence and stability of neural networks. By pursuing a modular approach, we interpret a cellular nonlinear network (CNN) as a positive feedback of a parallel block of single-input-single-output (SISO) dynamical systems, the neurons, and a static multiple-input-multiple-output (MIMO) system that couples them (typically the so-called interconnection matrix). The analysis extends previously known results by enlarging the class of allowed neural dynamics to higher order neurons.