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.

The development of artificial intelligence has made significant contributions to the financial sector. One of the main interests of investors is price predictions. Technical and fundamental analyses, as well as econometric analyses, are conducted for price predictions; recently, the use of AI-based methods has become more prevalent. This study examines daily Dollar/TL exchange rates from January 1, 2020, to October 4, 2024. It has been observed that among artificial intelligence models, random forest, support vector machines, k-nearest neighbors, decision trees, and gradient boosting models were not suitable; however, multilayer perceptron and linear regression models showed appropriate suitability and despite the sharp increase in Dollar/TL rates in Turkey as of 2019, the suitability of valid models has been maintained.