Spiking patterns and synchronization dynamics of thalamic neurons along the sleep-wake cycle are studied in a minimal model of four coupled conductance-based neurons. The model simulates two thalamic neurons coupled via a gap junction and driven by a synaptic input from a two-neuron model of sleep regulation by the hypothalamus. In accord with experimental data, the model shows that during sleep, when hypothalamic wake-active neurons are silent, the thalamic neurons discharge bursts of spikes. During wake, the excitatory synaptic input from the hypothalamus drives the coupled thalamic neurons to a state of tonic firing (single spikes). In the deterministic case, the thalamic neurons synchronize in-phase in the bursting regime but demonstrate multi-stability of out-of-phase, in-phase, and asynchronous states in the tonic firing. However, along the sleep-wake cycle, once the neurons synchronize in-phase during sleep (bursting), they stay synchronized in wake (tonic firing). It is thus found that noise is needed to reproduce the experimentally observed transitions between synchronized bursting during sleep and asynchronous tonic firing during wake. Overall, synchronization of bursting is found to be more robust to noise than synchronization of tonic firing, where a small disturbance is sufficient to desynchronize the thalamic neurons. The model predicts that the transitions between sleep and wake happen via chaos because a single thalamic neuron exhibits chaos between regular bursting and tonic activity. The results of this study suggest that the sleep- and wake-related dynamics in the thalamus may be generated at a level of gap junction-coupled clusters of thalamic neurons driven from the hypothalamus which would then propagate throughout the thalamus and cortex via axonal long-range connections.