The current study proposes a novel cognitive architecture for a computational model of the limbic system, inspired by human brain activity, which improves interactions between a humanoid robot and preschool children using joint attention during turn-taking gameplay. Using human-robot interaction (HRI), this framework may be useful for ameliorating problems related to attracting and maintaining attention levels of children suffering from attention deficit hyperactivity disorder (ADHD). In the proposed framework, computational models including the amygdala, hypothalamus, hippocampus, and basal ganglia are used to simulate a range of cognitive processes such as emotional responses, episodic memory formation, and selection of appropriate behavioral responses. In the currently proposed model limbic system, we applied reinforcement and unsupervised learning-based adaptation processes to a dynamic neural field model, resulting in a system that was capable of observing and controlling the physical and cognitive processes of a humanoid robot. Several interaction scenarios were tested to evaluate the performance of the model. Finally, we compared the results of our methodology with a neural mass model.