The Application Of Functional Equations In Artificial Neural Networks And Bio-Mathematics

Due to the broad spectrum applications in pattern recognition,automatic-control systems,image processing,optimization,signal processing,associative memories and so on, the artificial neural networks(ANN) have attracted so much attentions. Since it is important to avoid the spurious response or local minima in the application of ANN, the core problem is to investigate the global attractivity of the ANN.In fact, people carry out the functions of the ANN by using electrocircuit. Time delays can not be avoided because of the artificial factor,the finite switching speed of amplifiers and technic level, and so on. Besides, the ANN's theory based on the simulating to man brain, and it is well-known that people have two kinds memory: the long time memory(LTM) and the short time memory(STM). Based on these, we research the global attractivity of the time delayed competitive neural networks with different time scales in this paper.The latent period acts an important role in the dynamic model of epidemic. Currently, people often investigate the dynamic model of epidemic by using ordinary differential equations and without thinking the delays. So, in this paper we study the epidemical dynamic models which have time delays and latent period. And we find the results well-fitting to the reality when we test the situation of SARS and Birds-flu by applying this paper's conclusions.In chapter 1, we present several important definitions and theorems. And in the next chapter, we research the global asymptotic stability of almost periodic solution of retarded...