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## Butterfly chaos

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**Eman Abu Sumra**Butterfly chaos Physics department , faculty of science An-Najah National University Nablus, Palestine**Contents**• Introduction • Chaos definition and characteristics of chaos • History of chaos • Butterfly effect • Butterfly chaos theory • The butterfly effect in Loranez attractor and equations • Applications of chaos**Introduction**• What is the chaos theory? • When the chaos theory discovered and who discovered it? • What is the butterfly effect and the relation between it and chaos theory? • What is the life field which depend on butterfly chaos? • All of these questions we want to fiend answers for it in this lecture.**Chaos definition**Dictionary definition: is turmoil, turbulence primordial abyss and undesired randomness.**Chaos definition (cont)**• Chaos is: irregular motion of dynamical system that is deterministic, sensitive to initial conditions, and impossible to predict in the long term with any thing less than an infinite and perfect representation of analog values.(Flake)**Chaos definition(cont)**Chaos is sustained and disorderly-looking long term evolution that satisfies criteria and that occurs in a deterministic non linear system, (William, 1997) Chaos: the property that characterizes a dynamical system in which most orbits sensitive dependence.(Lorenz, 1993)**Origins of chaos**Chaos theory is rooted in mathematics and the natural sciences, social sciences, organizational scholars and phsychologists**History of chaos**1873-British Physicist James Maxwell said “when an infinitely small variation in the present state may bring about a finite time. 1898-Frensh mathematician Maxwell remarked that an error in initial conditions can render a systems long term behavior unpredictable. 1908-Frensh mathematician Henri emphasized that slight differences in initial conditions eventually can lead to large differences. making prediction (impossible)**Edward Lorenz and butterfly effect**Chaos wasn’t until 1963 the metrologist Lorenz of MIT published his paper “Non periodic flow” that chaos really took of. Lorenz created toy weather on his computer “less modeled than science” at that time. Using a set of twelve equations his computer the weather**Edward Lorenz and butterflyeffect(cont)**• In the winter of 1961, wanting to examine a sequence at greater length, Lorenz took shortcut • Instead of starting the whole run over, he started midway through • To give machine its initial conditions, he typed the numbers straight from the earlier print out.**Edward Lorenz and butterflyeffect(cont)**• When he came back an hour later, the sequence had evolved differently.**Edward Lorenz and butterflyeffect(cont)**• The new run should have exactly duplicated the original, why didn’t it? • In the computers memory, six decimal places were stored 0,56127. • Lorenz entered 0,506 assuming that difference-one part in a thousnd-was the inconsequential.**Edward Lorenz and butterflyeffect(cont)**• This effect came to be known as thebutterflyeffect. *The flapping of a single butterflyes Produces a tiny change in the state Of the atmosphere. Over a period of Time , what the atmosphere actually Does diverges from what have done. So, in a months time, a tornado that Would have devastated the Indonesian Coast doesn’t happen or maybe that Wasn’t going to happened,does* {Ian Stewart, does God ply Dice? the Mathematics of chaos}**Butterfly chaos**The butterfly effect is a symbol of chaos it is Simple and entertaining way of describing one component of the greater chaos theory namely : “sensitive dependence on initialconditions”**The butterfly effect in the Lorenz attractor**time 0 ≤ t ≤ 30 (larger) z coordinate (larger)**How to make use of butterfly effect theory**• Waking up thirty minutes earlier: If you woke up just 30 minutes earlier each day you will be able to do some new things such as exercising. After few weeks you will become more fit, your self image will improve and consequently your self confidence will. The improvement in your self confidence will positively affect your career, health and relationships!! That was another example of the butterfly effect theory. A very small change has produced very big results.**How to make use of butterfly effect theory (cont)**Getting rid of a false belief: Spending 10 minutes reading an article that can help you get over false belifes can result in improving your self confidence and increasing your chance of success. Again that's how the butterfly effect theory can help you improve your life