Before revision:  If the function satisfies constraints such as continuity and monotonicity, neural network under external stimulus would always go to fixed point, and there could be one-one-one mapping between external stimulus and synaptic strength at fixed point.
After revision:  If the function satisfies constraints such as continuity and monotonicity, neural network under external stimulus would always go to fixed point, and there could be one-to-one mapping between external stimulus and synaptic strength at fixed point.