We have found that single neuronal activities in different regions in the brain commonly exhibit the distinct dynamics transition during sleep-waking cycle in cats. Especially, power spectral densities of single neuronal activities change their profiles from the white to the 1/f along with sleep cycle from slow wave sleep (SWS) to paradoxical sleep (PS). Each region has different neural network structure and physiological function. This suggests a globally working mechanism may be underlying the dynamics transition we concern. Pharmacological studies have shown that a change in a wide-spread serotonergic input to these regions possibly causes the neuronal dynamics transition during sleep cycle. In this paper, based on these experimental results, an asynchronous and symmetry neural network model including inhibitory input, which represents the role of the serotonergic system, is utilized to examine the reality of our idea that the inhibitory input level varying during sleep cycle induce that transition. Simulation results show that the globally applied inhibitory input can control the dynamics of single neuronal state evolution in the artificial neural network: 1/f-like power spectral density profiles result under weak inhibition, which possibly corresponds to PS, and white profiles under strong inhibition, which possibly corresponds to SWS. An asynchronous neural network is known to change its state according to its energy function. The geometrical structure of network energy function is thought to vary along with the change in inhibitory level, which is expected to cause the dynamics transition of neuronal state evolution in the network model. These simulation results support the possibility that the serotonergic system is essential for the dynamics transition of single neuronal activities during sleep cycle.