The mathematical field of chaos theory has become a valuable resource for understanding complex systems that exhibit sensitive dependence on initial conditions. The creation of chaos theory, which has applications in a wide range of scientific domains, involved many scientists and mathematicians. It was originally created in the physical sciences to describe the behavior of dynamic systems. Applications of the chaos theory can be found in many different domains including economics, biology, social sciences and meteorology. This study investigates the basic ideas of chaos theory and its application in real life scenarios. It highlights the impact of chaos theory on various domains, emphasizing its relevance in predicting, understanding, and controlling complex systems and also presents an overview of chaos theory. In this study, we will go over chaotic systems, real-world uses for chaos theory, and chaos theory's drawbacks. We ultimately determine the chaos theory study report's conclusion.

Keywords: Chaos theory, Sensitive dependence on initial conditions (SDIC), Dynamical systems.

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