Qualitative Analysis Of Dynamic Neural Networks

Since the forties of the twentieth century, the study of artificial neural networks has ever been evolving for about half a century and it has attracted a large number of researchers in many different areas. Now artificial neural networks have become a frontier of encephaloneural science, mathematics and information science.Neural networks has the properties of a complex dynamic system, the prerequisite condition of it been used in many field is that it has some qualitative properties such as stability, convergence. In hardware implementation, however, time delays occur. In most situations, delays are variable and in fact unbounded. From the mathematical points of view, systems with constant delay are different from those with variable or unbounded delays. Time delays may lead to an oscillation and furthermore, to instability of networks. Therefore, the study of stability of delayed neural networks is practically needed.Reaction-diffusion cannot be avoided in the neural networks model because electrons are moving in asymmetric electromagnetic field, so we must consider the diffusion effect in reality design. From the view of biological neural networks, brain's behavior is periodic and chaotic oscillation. So it is worthy of analysis the qualitative properties of reaction diffusion system and periodic system.In artificial neural networks system, the neural activate functions decide the capacity of system. From the result of recent research, many of them are based on the assumptions of strictly increasing and bounded. Unfortunately, these assumptions make the results inapplicable to some important engineering problems.In this paper, without assuming the boundedness and monotonicity of the activate functions, even type of vector Lyapunov functions were constructed based on M-matrix theory to study the qualitative properties of dynamic neural networks with variable delays, unbounded delays, reaction-diffusion and periodic oscillation. A series of algebraic conditions that are independent of delays were obtained for stability. These conditions include the results in many researchers, and could be conveniently used in artificial neural networks design.