Stability Theory Of Neural Networks With Delay

This work deals with the stability theory of neural networks. A set of stability results for several general neural network models are derived via the Liapunov direct method and theory of monotone dynamic systems.As the introduction, in Chapter One, the background and history of neural networks are briefly addressed. The motivations, notations and outline of this work are also given in this chapter.In Chapter Two, Liapunov functional method and Liapunov function method with Razumikhin techniques are employed to obtain some delay independent stability results for the Cohen-Grossberg neural networks with multiply delays. In that sense, the delays are harmless.In Chapter Three, the stabilization role of self-inhibitory Cohen-Grossberg neural networks is studied. Using theory of monotone dynamic systems, the convergence results obtained for a class of special Cohen-Grossberg neural networks without delays are extended to the delayed cases provided the delays corresponding the negative self-connections are small enough in which an estimation for the smallness is also given.Exponential stability is investigated in Chapter Four for Cohen-Grossberg neural networks. Applying the theory of monotone dynamic system, the componentwise exponential stability is also obtained.In Chapter Five, some sufficient conditions with adjustable parameters are derived for the exponential stability of Cohen-Grossberg neural networks with memory.Stability and Hopf bifurcation for the bidirectional associative memory neural networks including the global and local stability are studied in Chapter Six.Finally, in Chapter Seven, the global exponential stability of the discrete-time neural networks with general activation functions is investigated.