A Neuro-Dynamic Mathematical Model of Dream Formation and Spontaneous Cognitive Activity

Abstract: This paper introduces a biomathematical model designed to describe the internal dynamics of dream formation and spontaneous cognitive processes. The model incorporates neurocognitive factors such as dissatisfaction, acceptance, forgetting, and mental activity, each of which is linked to established neural systems. We formulate a system of differential equations to simulate interactions among these variables and validate the model using simulated neural data. Our results demonstrate biologically plausible cognitive patterns consistent with findings from EEG and fMRI studies, particularly related to the default mode network (DMN), anterior cingulate cortex (ACC), and hippocampal memory mechanisms.