<b>A Study of Firefly Algorithm and its Application in Non Linear Dynamic Systems</b> Firefly Algorithm FA is a newly proposed computation technique with inherent parallelism, capable for local as well as global search, meta heuristic and robust in computing process. In this paper, Firefly Algorithm for Dynamic System FADS is a proposed system to find instantaneous behavior of the dynamic system within a single framework based on the idealized behavior of the flashing characteristics of fireflies. Dynamic system where flows of mass and or energy is cause of dynamicity is generally represented as a set of differential equations and Fourth Order Runge Kutta RK4 method is one of used tool for numerical measurement of instantaneous behaviours of dynamic system. In FADS, experimental results are demonstrating the existence of more accurate and effective RK4 technique for the study of dynamic system. FADS, Firefly Flashing, First Order Differential Equations, RK4 542-549 Issue-2 Volume-2 Gautam Mahapatra | Srijita Mahapatra | Soumya Banerjee