Absence epilepsy, characterized by 2-4 Hz spike-wave discharges (SWDs), can be caused by pathological interactions within the thalamocortical system. Cortical spindling oscillations are also demonstrated to involve the oscillatory thalamocortical rhythms generated by the synaptic circuitry of the thalamus and cortex. This implies that SWDs and spindling oscillations can share the common thalamocortical mechanism. Additionally, the thalamic reticular nucleus (RE) is hypothesized to regulate the onsets and propagations of both the epileptic SWDs and sleep spindles. Based on the proposed single-compartment thalamocortical neural field model, we firstly investigate the stimulation effect of RE on the initiations, terminations, and transitions of SWDs. It is shown that the activations and deactivations of RE triggered by single-pulse stimuli can drive the cortical subsystem to behave as the experimentally observed onsets and self-abatements of SWDs, as well as the transitions from 2-spike and wave discharges (2-SWDs) to SWDs. In particular, with increasing inhibition from RE to the specific relay nucleus (TC), rich transition behaviors in cortex can be obtained through the upstream projection path, RE→TC→Cortex. Although some of the complex dynamical patterns can be expected from the earlier single compartment thalamocortical model, the effect of brain network topology on the emergence of SWDs and spindles, as well as the transitions between them, has not been fully investigated. We thereby develop a spatially extended 3-compartment coupled network model with open-/closed-end connective configurations, to investigate the spatiotemporal effect of RE on the SWDs and spindles. Results show that the degrees of activations of RE1 can induce the rich spatiotemporal evolution properties including the propagations from SWDs to spindles within different compartments and the transitions between them, through the RE1→TC1→Cortex1 and Cortex1→Cortex2→Cortex3 projecting paths, respectively. Overall, those results imply that RE possesses the pacemaker function in controlling SWDs and spindling oscillations, which computationally provide causal support for the involvement of RE in absence seizures and sleep spindles.