A Scalable Framework with Modified Loop-Based Multi-Initial Simulation and Numerical Algorithm for Classifying Brain-Inspired Nonlinear Dynamics with Stability Analysis

The principal problem with the analysis of nonlinear dynamical systems is that it is repetitive and inefficient to simulate every initial condition and parameter configuration individually. This not only raises the cost of computation but also constrains scalability in the exploration of a large parameter space. To solve this, we restructured and extended the computational framework so that variation in the parameters and initial conditions can be automatically explored in a unified structure. This strategy is implemented in the brain-inspired nonlinear dynamical model that has three parameters and multiple coupling strengths. The framework enables detailed categorization of the system responses through statistical analysis and through eigenvalue-based assessment of the stability by considering multiple initial states of the system. These results reveal clear differences between periodic, divergent, and non-divergent behavior and show the extent to which the strength of the coupling kij can drive transitions to stable periodic behavior under all conditions examined. This method makes the analysis process easier, less redundant, and provides a scalable tool to study nonlinear dynamics. In addition to its computational benefits, the framework provides a general method that can be generalized to models with more parameters or more complicated network structures.