# Explaining the Chaos Theory

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Chaos Theory Chaos theory is a modern development in the math and science field to provide a frame work for understanding the irregular fluctuations in nature. Chaos is typically defined as mathematical property of the dynamic system. The study of their dynamics is an essential part of the growing science of complexity. There are some examples that explained what the chaos theory is like “the butterfly effect” and the “pendulum swing” that show an erratic behavior of the chaos theory. To understand the chaos theory’s principles of that underlie pattern of all real systems; they research from the ecosystems to the social systems to the universe as a whole. It is defined to show sensitivity to initial conditions. When the initial conditions started out small, it will rapidly lead to growing error in any effort to predict the future’s behavior. Measurement is not indefinitely precise but the motions and the patterns should be observed where it should be. Therefore, chaos theory is a theory that develops in the math and science field to provide the understanding of frame work in the erratic fluctuations that is found in nature. In chaos theory in the math field, they have a dynamical system that determine the sensitive dependence on initial conditions on closed invariant points and they’re close together separately over time at the continuous rate. They are deterministic mathematical models that give unique evolution that changes in variables and describe the target system. They are considered as linear or nonlinear depending on the nature of the equation of motion in the relating target system. In the chaotic solution, the deterministic equation means a solution that will come out sensitive based on the initial conditions and the ... ... middle of paper ... ...ic system based on the initial conditions that leads to a continuous outcome in random. The butterfly effect and the pendulum show great examples of a chaos theory because of their unpredictable motion. Not to mention, the butterfly effect tells the butterfly wings are the initial conditions; and one flap of its wing could set a tornado in Kansas or Texas. It helps for the scientist to predict the weather pattern if they looked more closely. For the pendulum, it shows unpredictable motion when it’s pushed and swings freely. The pendulum has a limited cycle when there are two pendulums that bumps into each other and their dynamic system change it completely. Therefore, the chaos theory is defined as an erratic behavior in the dynamic system, looking for patterns in weather or graphs to understand the irregular fluctuations in nature and predicts the future behavior.