The Generation Of Coexisting Chaotic Attractors And Design Of Chaotic Circuit Based On Memristor

The memristor is proposed by L.O.Chua in 1971 and a solid state implementation of the memristor is fabricated in HP laboratory in 2008.It is rapidly attracting the attention of researchers because of its unique memory properties and nano-scale size.The chaotic circuit designed by using the memristor is easy to generate high frequency chaotic oscillators and it will be widely used in the field of image encryption and secure communication.Constructing chaotic circuit with memristor is an important research direction at present.In the past,most of the constructed chaotic circuits contain only one or two memristor and if design the high-order chaotic circuits with multiple memristor,it has many circuit parameters and very complex topological structure,which enhances the complexity of chaotic system and the randomness of the generated signal,so it will have better security performance and safety performance in chaotic secure communication.In this paper,a lot of work has been done,and the main research results are given as follows:1)A floating memristor chaotic circuit with the serial connection between a charge-controlled memristor and an inductor is proposed,the memristor uses a PWL model.Basic dynamic properties of the system are investigated by conventional dynamic analysis method,and it shows that the system can produce a pair of "heart" type attractors about origin symmetry.The Hopf bifurcation behavior is analyzed and verified by numerical simulation.Differently,the most remarkable feature of the citcuit is that it adopts a floating memristor,and with different initial state,it can also generate nonlinear phenomena including coexisting chaotic and coexisting chaotic-periodic attractors.2)A six-order chaotic circuit is proposed,the circuit is mainly composed of three parts: the parallel connection between a flux-controlled memristor and capacitor,the serial connection between a charge-controlled memristor and inductor,and another flux-controlled memristor is alone and floating,which enriches the application of memristor in high-order chaotic circuit.The dynamic properties of the circuit are demonstrated in detail.Equilibria and equilibria stability analysis show that the circuit has an equilibrium set locating in the three-dimensional space which is constituted by memristor internal state variables,and it is found that the equilibrium stability is decided by the circuit parameters and the initial state of three memristors.The Lyapunov exponent spectra and bifurcation diagrams of the circuit imply that it canproduce two bifurcation behaviors by adjusting its parameters,which are Hopf bifurcation and anti-period doubling bifurcation,and the hyperchaos,transient chaos and intermittency cycle phenomena are found in the same system.3)The attractor is producted by the fourth and sixth order chaotic circuits which designed in this paper is studied.When voltage and electricity signal in observing chaotic attractors are extended to power and energy signal,the simulation results indicate that some strange attractors like bow tie type are observed in the fourth order chaotic circuit.In the six-order chaotic circuit,the simulation results imply that some strange attractors like lotus type and superposition type are observed when it is used by the same method,and the Attractor production between the energy signals of the memristors are studied.Specially,the coexistence of chaotic attractors is observed by using the power and energy signals to study the coexistence phenomena of the system.