Behavior Analysis of an HMR Neuron and Comparison with Multiple Coupled HMR Neurons

System Analysis plays a crucial role in understanding the functional structure, analyzing the periodic behavior of biological systems, model validation, pattern generation, and controller design in a minimal neural network. Therefore, system analyses including the location and type of equilibrium points, stability, and dynamic behaviors in various scenarios for an isolated HindMarshRose neuron as well as two HMR neurons with their interconnections are simulated and investigated. In this article, a network of two identical neurons with different couplings is examined and the relationship between the dynamic regimes of an isolated neuron and simultaneous regimes in the model of two coupled neurons is explored in various scenarios. In this article, a comprehensive system analysis has been conducted for the first time to interpret dynamic behavior, establish patterns, and understand collective behavior in a neural network. The impact of factors such as the value and type of external stimulation signal, the value and direction of coupling, and the initial conditions of neurons have been explored. Numerical simulation is conducted for comprehensive analysis. Results can assist therapists in applying the correct external stimulation signal to achieve dynamic and therapeutic behavior in the neural network.