Dynamics Analysis And Sliding Mode Control Of Fractional-order Memristor-based Chaotic Circuit System

Chaos involves in many fields such as natural science and social science,it is the forefront of science in the world,it can be say that the dynamics and applications of chaotic circuits are the core problem of chaos.As a new nonlinear circuit component,memristor has a great application prospect in many fields such as chaotic circuit,chaotic encryption and so on.With the development of memristor,the memristive chaotic circuit has received the widespread attention at domestic and abroad.Draw support of simple memristor circuit's modeling and analysis,the basic characteristics of chaotic circuit can be studied effectively.In the recent years,researches have shown that fractional calculus is more accurate and efficient than traditional integer calculus in describing some physical phenomena,thus,fractional theory is applied in the memristive chaotic system.The experimental results show that in the fractional-order memristor-based chaotic circuit,it can not only study the rich chaos phenomenon,but also can make use of or control the chaos.In this paper,based on the complex dynamics of memristive chaotic system,a fractional-order memristive chaotic system deriving from the integer-order counterpart is deduced,and its dynamics has been studied in depth.Furthermore,chaos is applied in the watermark encryption algorithm,which can effectively improve the confidentiality of the algorithm.Finally,for purpose of suppressing the occurrence of chaos,a fractional slide model controller is proposed.The main innovations are as follows:(1)Based on the simple integer-order memristor chaotic circuit,the dynamic model of the fractional-order memristive chaotic circuit is established.The stability of the chaotic circuit is analyzed based on Lyapunov exponent indirect method.Meanwhile,nonlinear dynamic phenomena is focused on.Under the different system control parameters,bifurcation,diagram and the Lyapunov exponent are used to study the chaotic phenomena of fractional-order memristive system.(2)Based on sensitivity to the initial value and complex chaotic phenomenon of fractional order chaotic systems,fractional order chaotic system is used to encrypt digital watermarking image,and discrete wavelet transform algorithm is proposed to embed and extract encrypted watermarking.In order to prove the security of the algorithm,anti-aggressive and sensitivity to the key are analyzed in detail.The experimental results show that the watermark algorithm based on fractional order chaotic system has high security,invisibility compared with the previous work.(3)With fractional order memristive chaotic system as the research object,a fractional order sliding mode controller is designed to suppress chaos.In order to ensure the occurrence of sliding mode behavior,a integral type sliding mode surface is chosen based on combining the Lyapunov stability theorem and the sliding mode theory.Then the sliding mode controller under the method of function switching control is designed,and the condition that designed controller's parameters should be followed is deduced.The stability of controlled system which under the different parameters of controller is analyzed by experimental results,and time domain waveform figure is get to verify the correctness of the theoretical analysis.