Butterfly effect is a term that defines the more stringent concept of “sensitive dependence on the initial state of a nonlinear dynamical system” in chaos theory: slight changes in the initial state of the system can make big changes in the long term of its behavior; sometimes presented as unpredictable (chaotic) behavior, demonstrated by very simple systems
The term comes from the idea that butterfly wings can create tiny changes in the Earth’s atmosphere that can ultimately change the tornado’s path or delay, accelerate, or even prevent tornadoes from occurring in a specific place at a specific time. The oscillating wing represents a trifle in the initial state of the system, which causes a chain of events leading to events with large-scale changes. If the butterfly did not flap its wings, the trajectory of the system would probably be completely different. Of course, a butterfly cannot literally cause a tornado. The kinetic energy in a tornado is extremely greater than the energy of a butterfly. The kinetic energy of a tornado is ultimately provided by the sun, and a butterfly can only affect chaotic manner in certain details of weather events.
“Only an approximate return of the system to its initial state”, as well as “the sensitive dependence of the system on the initial state” are the two main components of chaotic motion. They have a practical consequence in modeling complex systems, such as weather: it is difficult to predict their behavior beyond a certain time range (approximately a week in the case of weather).
