General inter-connected neural network: the analysis of its stability

Neural network which is formed by extensive interconnections of neurons performing simple functions, is a complicated nonlinear dynamic system. By now the stability of neural network systems has only been analysed on those with restricted connection forms such as symmetrical feedback and feedforward networks, with their sufficient conditions of stability given. Based upon nonlinear system theory, this paper studies neural network system with general connective forms, giving the sufficient conditions of globally asymptotic stability of network. The locally asymptotic stability of the equilibration solutions of multistable-state is also discussed.