Brain information processing is shaped by fluctuations in neuronal rhythmic activities, each defining distinctive brain states. Switches in brain states during wake-sleep cycle are described at the network level, by a neuronal population shift from active to oscillatory state. At the cellular level, neurons switch from tonic to burst. This switch is organized thanks to neuromodulators. They refer to signaling molecules that induce reversible changes in functional properties of neurons or synapses. Simultaneously, learning and memory are attributed to the ability of neurons to modify their connections based on experience, a property called synaptic plasticity. It exploits the correlation level in the activity of connected neurons. Altogether, sleep contributes to memory, a phenomenon called sleep-dependent memory consolidation. Experimental results show a down-selection mechanism i.e., strong (resp. weak) connections established during wakefulness are preserved (resp. decreased) during sleep. However, little is known about its underlying physiological processes. This research leads the way to uncover biological explanations. Using a conductance-based model robust to neuromodulation and synaptic plasticity, we built a cortical network to study the evolution of synaptic weights during switches in brain states. We tested several types of synaptic plasticity rules such as triplet and calcium-dependent models. We reproduced experimental data acquired in wakefulness. Then, switching the network from tonic to burst without any modification of the synaptic rule leads to a homeostatic reset. All synaptic weights converge towards the same basal value whatever the rule due to neuromodulation of neuronal activity. We showed that neuromodulation of synaptic rules is necessary to overcome this reset. For triplet models, the spike-time dependent curve is deformed as demonstrated in [Gonzalez-Ruedas,2018]. For calcium-based models, calcium thresholds are neuromodulated or the potentiation level is weight-dependent due to neuromodulatory markers. The neuromodulated-synaptic rules are shown to support the down-selection mechanism during sleep, avoiding the homeostatic reset.