Barishal University Journal Part 1, 5(1&2): 123-140 (2018) ISSN 2411-247X 123 CHAOS THEORY AND ITS APPLICATIONS IN OUR REAL LIFE Hena Rani Biswas *,1 , Md. Maruf Hasan 2 and Shujit Kumar Bala 1 1 Department of Mathematics, University of Barishal, Barisal -8200 2 Department of Mathematics, Comilla University, Cumilla-3506 Abstract Chaos theory is a mathematical field of study which states that non-linear dynamical systems that are seemingly random are actually deterministic from much simpler equations. Chaos theory was developed by inputs of various mathematicians and scientists; its applications are found in a large number of scientific fields. The purpose of this paper is to provide an introduction to chaos theory together with fractals, the elaborate patterns which have become its emblem. This paper we discuss chaotic systems, Fractals and its application, real life application of chaos theory and limitations of chaos theory. Finally we establish the idea of control of chaos. Keywords: Chaos theory, Fractals, Sensitive dependence on initial conditions (SDIC) Introduction The word Chaos comes from the Greek word “Khaos”, meaning “gaping void”. Mathematicians say it is tough to define chaos, but is easy to “recognize it when you see it.” Chaos in other words means a state of total confusion or predictability in the behavior of a complex natural system. Chaos theory (Devaney 1989) is the concept that a small change now can result in a very large change later. It is a field of study in mathematics, with applications in several disciplines including physics, engineering, economics, biology (Morse 1967), and philosophy which primarily states that small differences in initial conditions (such as those due to rounding errors in numerical computation) can yield widely diverging outcomes for chaotic systems, rendering long-term prediction impossible in general. I hope that this paper serves as a useful tool for anyone who is interested in understanding this topic. Chaos theory is one of the fundamental theories in our lives. It is the study of complex, nonlinear dynamic systems. It is a branch of mathematics that deals with systems that * Corresponding Author’s e-mail: biswas.hena@yahoo.com