Multistability Analysis Of Two Kinds Of Neural Network Models

Neuron activity is an extensive phenomenon in human life and whole nature. Neural network system is a complicated network system consisting of large numbers of simple neurons. In recent years, academic researches for neural network system play an important role in martial and civil fields and closely link with capacity network design, fuzzy logic, numerical value computation and differential equation etc.. The investigation target and history of the neural network, Hop-field type neural network, transfer function and stability in the network together with some correlative results are introduced in Chapter 1.Chapter 2 is mainly devoted to the case of planar 2-D system, including the autonomic system with existence and uniqueness condition of solution, and its linearization equation. Then, non-degenerate equilibrium of the linearization system and its stability are detailedly studied. The degenerate equilibrium of this system is also simply introduced.In Chapter 3, multistability in a class of 1-D Hopfield neural network with Sigmoid-transfer function is studied. Stability is one of the most important properties of neural networks. In recent years, many good results have been got on mono-stability of Hopfield neural network with special Sigmoid-transfer functions. However, it is difficult to get the solutions of a system with a general Sigmoid-transfer function because of its general formed transfer function, not mentioning its multistability. Therefore, there are few results about multistability of the system with a general formed Sigmoid-transfer function. In...