A Brief Review of The Development of The Theory of Dynamical Systems (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.
Keywords: Dynamical Systems; Poincaré‟s contribution; Mathematical Modeling and Analysis; Aleksandr Lyapunov contribution; David Birkhoff Contribution