(untitled) (Journal of Mathematical Modeling and Fractional Calculus, 2026)
In this paper, we present a brief analysis of the evolution of theories of dynamical systems applied in various mathematical Models. In this study, the contributions of some notable mathematicians have been extensively discussed in the context of multiple applications of mathematical theories to dynamical systems. The investigation of the stability of periodic solutions, the stability of equilibrium, and Poincaré‟s periodicity has also been discussed in this paper. Moreover, an extensive study has been carried out on a brief application of the Poincaré Maps, the Last Geometric Theorem, the Restricted Three-Body Problem, the Generalized Hopf bifurcation, and the Van der Pol and Lienard equation for various mathematical models applied in dynamical systems.