We propose two distinct types of norepinephrine (NE)-neuromodulatory systems: an enhanced-excitatory and enhanced-inhibitory (E-E/E-I) system and a depressed-excitatory and enhanced-inhibitory (D-E/E-I) system. In both systems, inhibitory synaptic efficacies are enhanced, but excitatory ones are modified in a contradictory manner: the E-E/E-I system enhances excitatory synaptic efficacies, whereas the D-E/E-I system depresses them. The E-E/E-I and D-E/E-I systems altered the dynamic property of ongoing (background) neuronal activity and greatly influenced the cognitive performance (S/N ratio) of a cortical neural network. The E-E/E-I system effectively enhanced S/N ratio for weaker stimuli with lower doses of NE, whereas the D-E/E-I system enhanced stronger stimuli with higher doses of NE. The neural network effectively responded to weaker stimuli if brief γ-bursts were involved in ongoing neuronal activity that is controlled under the E-E/E-I neuromodulatory system. If the E-E/E-I and the D-E/E-I systems interact within the neural network, depressed neurons whose activity is depressed by NE application have bimodal property. That is, S/N ratio can be enhanced not only for stronger stimuli as its original property but also for weaker stimuli, for which coincidental neuronal firings among enhanced neurons whose activity is enhanced by NE application are essential. We suggest that the recruitment of the depressed neurons for the detection of weaker (subthreshold) stimuli might be advantageous for the brain to cope with a variety of sensory stimuli.