Multistability Analysis Of Memristive Hidden Oscillation And Its Applications

Memristor is a nonlinear element with memory function.The memristor can be used to construct a chaotic system with high complexity and multistability characteristics,resulting in more complex dynamics.Correspondingly,the application value of chaotic signals in the fields of image encryption and secure communication is also improved.In recent years,more and more hidden chaotic attractors have been discovered.Compared with the general chaotic systems,hidden chaotic oscillations are more concealed and more suitable for image encryption.Therefore,the design of hidden chaotic systems based on memristor is a very meaningful research topic.Based on the research on hidden chaotic systems,memristive hidden chaotic systems and conditional symmetric chaotic systems,a series of conditional symmetric hidden chaotic systems and a memristive hidden chaotic system are proposed,and the two types of hidden chaotic systems are studied in the image encryption.The main contributions are summarized as follows:Firstly,the conditional symmetrization modeling rule of attractor of hidden chaotic system is discovered,revealing the attractors coexisting in the system.By using the symmetry of nonlinear functions,the new polarity balance of the systems is obtained,and the conditional symmetric hidden chaotic systems are proposed.Through simulation,the phase diagrams,Lyapunov exponents,bifurcation diagram of the system are obtained,and the dynamic analysis of the system is carried out,which verifies the construction method of system condition symmetry.The analog circuit of partially hidden chaotic systems are realized by using the analog unit circuit,and the dynamic behavior of the systems is verified.Secondly,the memristive hidden chaotic system is proposed,and the newly proposed chaotic system has the characteristics of intermittent chaos and hypermultistability.By simulating the phase diagrams,Lyapunov exponents and bifurcation diagram,the dynamics of the system is analyzed in detail.The dynamic analysis shows that the system has infinite linear equilibria and presents intermittent chaotic characteristics and phenomenon of hypermultistability.The memristive hidden chaotic system and the memristor are simulated by using simulation software PSpice,and the expected experimental results are obtained.In addition,an appropriate discrete algorithm is used to discretize the continuous system equations,and a digital circuit platform is built to verify the complex chaotic behavior of the system.Finally,the application of hidden chaotic system and memristive hidden chaotic system in image encryption is studied.Because hidden chaotic attractor has greater concealment and unpredictability,the above two types of hidden chaotic signals are combined with DNA coding and operations to be applied to image encryption.The security performance of image encryption is analyzed,including key space,key sensitivity,pixel histogram of the image before and after encryption,information entropy and neighboring pixel correlation,etc.,and for the security of encryption,compared with the algorithms proposed in related literature.