Markovian jump delayed Hopfield networks with multiplicative noise

A non-symmetric version of Hopfield networks subject to state-multiplicative noise, pure time delay and Markov jumps is considered. Such networks arise in the context of visuo-motor control loops and may, therefore, be used to mimic their complex behavior. In this paper, we adopt the Lur’e–Postnikov systems approach to analyze the stochastic stability and the L2L2 gain of generalized Hopfield networks including these effects.