Systems with slope restricted nonlinearities and neural networks dynamics

Abstract

The quite large standard class of additive neural networks is considered from the point of view of the qualitative theory of differential equations. Connections with the theory of absolute stability are pointed out and a new class of Liapunov functions is introduced, starting from the positiveness theory (Yakubovich-Kalman-Popov lemma). The results are valid for a quite large class of dynamical systems and they are tested on some neural network structures. In the concluding part some perspective research is mentioned, including synchronization and time-delay effects. © 2011 Springer-Verlag.