ABSTRACT
Chaos is common in nature. ¥e earliest discovery of chaotic behavior can be casted back to Poincare, aFrenchmathematicianinthenineteenthcentury.Inhisstudyofcelestialmechanicsofconservative system,Poincarefoundthatsomesolutionsofadeterministicdynamicequationwereunpredictable. ButtheresearchworkonchaosisusuallysaidtobeginwithLorenz[L63],anAmericanmeteorologist. Whenhewasworkingontheproblemofweatherpredictionusingcomputer,hefoundthatthesolution ofadeterministicdynamicequationwithcertainparameterscanberandom-liked.¥isphenomenon cametobeknownasthebutter®yeªect.A¯erthen,Henon[H76]andRossler[R79]obtainedsimilar conclusions.Sincethen,chaostheoryhasbecomeoneofthemostpopularresearchtopicsandgreat development has been made in chaos science.
