Before revision:  If the function satisfies constraint such as continuity and monotonicity, neural network  would always go to one unique fixed point. A biological image classifier is proposed to utilize this fixed point .
After revision:  If the function satisfies constraint such as continuity and monotonicity, neural network would always go to fixed point, and there could be one-one-one mapping between external stimulus and synaptic strength at fixed point. In other words, neural network "memorizes" external stimulus in its synapses. A biological classifier is proposed to utilize this fixed point .