Stochastic differential equations (SDEs) are mathematical models that describe how systems evolve over time in the presence of random noise or uncertainty. These equations are used in a wide range of fields, including physics, biology, finance, and engineering, to study the behavior of complex systems that are influenced by random fluctuations. In a stochastic differential equation, the rate of change of a system's state at any given time is determined by a deterministic term, which represents the system's expected evolution, as well as a stochastic term, which accounts for random fluctuations. The dynamics of the system are thus described by a combination of both deterministic and random processes. The study of stochastic differential equations involves not only finding solutions to these equations but also analyzing the long-term behavior and stability of systems described by them. Researchers use a variety of analytical and computational techniques to study SDEs and gain insights into the behavior of stochastic systems. Overall, stochastic differential equations provide a powerful framework for modeling and analyzing the dynamics of complex systems that are subject to random fluctuations, making them a valuable tool in many scientific and engineering disciplines.