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 evolution will phase through space that will appear to be random. If there are small initial conditions, it may lead to greater differences in outcome. In dynamic system, they are described by having a very dense collection of points in periodic orbits and topologically transitive. It is being complex to initial condition of the dynamic system, a property that is known as “the butterfly effect.” However, there are chaotic system that does not have periodical orbits because they have to survive the boundaries KAM tori and sufficiently for a strong perturbations from the case. The terms “chaotic dynamics” refer to only the evolution of the system through time like the butterfly effect. To emphasize, the dynamical system in the chaos theory displays a sensible dependence on the initial conditions on random appearances followed by the evolution that phases through space.
In chaos theory, the butterfly effect was used to determine the nonlinear system that can result in huge differences in later state which looks like the Lorenz attractor. The butterfly effect happens in the weather processes to have strong dependence on the outcome and very slightly different from the initial conditions. In 1963, Edward Lorenz, studied...