Chaotic Nonlinear Transform Research Based On Chua's Circuit

Chaos is a special kind of movement in nonlinear dynamic system, which hassensitivity to initial conditions, long-term unpredictability, similarity to noise and othercharacteristics. It is very suitable for security communication, and in recent years, itbecomes a popular topic that is worth researching. As the communication security needsa lot of chaotic signals, more species and better characteristics of the chaotic signals forencryption are in urgent need.This paper mainly discusses the development of the chaos and the present situationof researching the chaotic circuit from home and abroad and introduces some importantapplications of chaos in details. It also discusses the basic theory and characteristics ofchaos system and the methods of identifying chaotic signals. The methods ofresearching chaos sensitivity to initial conditions are proposed. Power spectrum methodis used to study the influence of the nonlinear transform on the signal frequency. At thesame time, according to the complexity of the hardware circuit, p（x）=k₂x²+k₃x³is chosenas the nonlinear transform formula. Lyapunov exponent is used to study the best rangeof the nonlinear transform formula coefficient, to design the hardware circuit, aiming atp（x）=k₂x²+k₃x³, to do a lot of numerical simulations and physical experiments based onChua’s chaotic signals of the electric circuit system, and to compare the chaotic signalsbefore and after in many different aspects. Through the different changes of nonlineartransform circuit parameters, different chaos waveforms can be got and can producemore and better chaotic signals characteristics.Finally, the paper introduces the chaotic communication principle, and comparesthe original Chua’s chaotic signals and the nonlinear transform chaotic signals. Theresult proves that the chaotic signals after transform are more suitable for the encryptionof signals. The nonlinear transform to chaos can not only produce a lot of chaoticsignals, but also improve the chaos characteristics, to provide more chaotic signalsgenerators for secure communications.