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In this work, the researchers for computing an exact solution of the (2[Formula: see text]+[Formula: see text]1) dimensions Kundu–Mukherjee–Naskar (KMN) equation used a newly developed technique, namely, the new extended direct algebraic method. This powerful method gives an exact solution to the KMN equation considered in this paper. The results are new and attest to the efficiency of the proposed method.

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Introduction:One of the interesting topics in neuroscience is problem solving and decisionmaking. In this area, everything gets more complicated when events occur sequentially. One of the practical methods for handling the complexity of brain function is to create an empirical model. Model Predictive Control (MPC) is known as a powerful mathematical-based tool often used in industrial environments. We proposed an MPC and its algorithm as a part of the functionalities of the brain to improve the performance of the decision-making process. Methods:We used a hybrid methodology whereby combining a powerful nonlinear control system tools and a modular fashion approach in computer science. Our hybrid approach employed the MPC and the Object-Oriented Modeling (OOM) respectively. Therefore, we could model the interaction between most important regions within the brain to simulate the decision-making process. Results:The employed methodology provided the capability to design an algorithm based on the cognitive functionalities of the PFC and Hippocampus. The developed algorithm applied for modulation of neural circuits between cortex and sub-cortex during a decision making process. Conclusion:It is well known that the decision-making process results from communication between the prefrontal cortex (working memory) and hippocampus (long-term memory). However, there are other regions of the brain that play essential roles in making decisions, but their exact mechanisms of action still are unknown. In this study, we modeled those mechanisms with MPC. We showed that MPC controls the stream of data between prefrontal cortex and hippocampus in a closed-loop system to correct actions.