Neutrosophic-Plithogenic Dynamical Systems: Foundations, Stability, Partial and Refined Attractors / Neutrals / Repellers, and Chaos

Classical dynamical systems describe the evolution of states through deterministic or stochastic laws. However, many real-world systems involve uncertainty, contradiction, incompleteness, and indeterminacy that cannot be adequately represented within traditional frameworks. This paper introduces Neutrosophic-Plithogenic Dynamical Systems (NPDS), extending classical dynamics through neutrosophic states and plithogenic contradiction structures. A system state is represented by the neutrosophic triple <T, I, F>, where T, I, and F denote truth, indeterminacy, and falsehood components. Plithogenic attributes and contradiction degrees are then incorporated into the dynamics. New concepts are introduced, including neutrosophic attractors, neutrosophic repellers, neutrosophic neutral sets, neutrosophic partial attractors, neutrosophic partial repellers, neutrosophic Lyapunov exponents, and neutrosophic chaos measures. The resulting framework provides a natural mathematical representation for systems whose behavior is simultaneously attractive, neutral, and repulsive. Applications to scientific theory evolution, social systems, economics, artificial intelligence, and complex decision processes are discussed. The concepts of Partial Attractors, Partial Neutrals, Partial Repellers and respectively of Refined Attractors, Refined Neutrals, Refined Neutral Sets, were introduced by F.Smarandache in 2026, and they are richer and closer to reality than the ordinary classical versions of Attractors, Repellers.