Research On Models Of Memristor And Meminductor And Their Applications In Chaotic Circuits And Digital Watermarking

In 1971,Chua reasoned from the integrity of circuit relationship that there should be a fourth fundamental element,given the definition of memristor.Then,the real existence of memristor was proved by a team of researchers at HP laboratory when they were doing research on a nano thin film of TiO2 in 2008,having triggered wide attention of researchers and promoted the development of the memristor.In 2009,the family of memory elements was enriched by proposing the concept of meminductor.Meminductor is a new kind of non-linear inductor with memory feature,and has potential applications in nonvolatile memory,artificial neural network and other fields.So the family of memory elements such as meminductor is rapidly becoming a new research hotspot.At present,the study of meminductor is merely at initial stage,and no actual device has been realized,so the pre-research of meminductor is important and perspective.In this paper,we propose a novel mathematical model of meminductor and set up the equivalent circuit model to represent actual meminductor for experimental and applied research.A new type of chaotic oscillation system is designed based on the model of meminductor.We also analyze the dynamical behavior of chaotic systems and the randomness of the chaotic sequences and apply the chaotic encryption to the digital watermarking,proposed a digital watermarking algorithm based on DWT.We designed an image digital watermark embedding and extraction of application software based on Android platform.The main research contents of this paper are shown as follows:(1)Based on the model of HP memristor,a quadratic smooth mathematical model of meminductor is designed for studying the features and applications of meminductor,despite real meminductors have not been realized.In order to prove the feasibility of the circuit with hardwire experiments,we design the equivalent circuit model of the meminductor by using the existing operational amplifier and multiplier and simulate the circuit model and analyze the feature under different frequency and type input signal,such as sine wave square wave and triangle wave and find theirs relationship between current and magnetic flux are completely in accord with the typical hysteresis characteristic under different input signals.(2)In order to extract chaotic sequences with good random performance,a novel single easily implemented chaotic system is designed based on the designed meminductor.We have researched and analyzed the dynamics behavior of the chaotic system including getting unstable saddle points by the dissipativeness of system and the stability of equilibrium points,getting the dependence of the system on bifurcation parameters by the Lyapunov exponent spectrum bifurcation diagrams and dynamic map,and analyzing the relationship between system and initial value by attractive basin.Compared with other chaotic systems,this system has rich dynamic characteristics and special properties,such as homogeneous coexisting attractors and non-homogeneous coexisting attractors.The meminductor chaotic system is digitized by using DSP technology,and the chaotic sequence generated by this way was tested by NIST(National Institute of Standard and Technology).The randomness of the sequence is better than the traditional Logistic chaotic map and can be used for communication encryption field.(3)Because of the chaotic sequence can effectively eliminate the self correlation and improve the security of watermark information,the color image digital watermarking algorithm based on chaotic encryption and DWT is proposed by combining chaos theory with the digital watermarking.The way above can be used for significative watermark information and improve the security of the watermark.Based on the popular Android platform,a color image digital watermarking technology is designed to facilitate the user to embed and extract image ingormation.