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This research investigates the unexplored domain of negative parameters within dynamic systems, focusing on their influence across stability, traffic intensity, and chaotic phases. Using an iterative computational framework, we examine the sigma function (σ) to characterize system responses under varying conditions of and Visualizations and insights demonstrate transitions between phases for a first-ever exploration of negative values of the number of phases (k), with novel findings that extend foundational studies. This work establishes a baseline for further explorations of negative parameter spaces in complex systems. It is worth noting that the current work makes new contributions to Ismail’s contemporary Pointwise Stationary Fluid Approximation (PSFFA) theory by providing a comprehensive computational framework for exploring dynamic system behavior across varying parameter values.
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