The Design And Analysis Of New Chaotic Circuits Based On Memristors

In 1971,Professor Chua of the University of California,USA,predicted the presence of memristor based on the completeness of circuit theory.Until 2008,HP laboratories developed physical memristor with nano-materials,which caused widespread concern on memristor both at home and abroad.The memristor has nonlinear resistor with memory function and is very easy to generate chaotic oscillating signal.The chaotic system proposed based on memristor has more complex dynamical behaviors than the traditional chaotic system.The signal of chaotic system based on memristor has stronger pseudo-random performance,which makes it enjoy more widely application in the bioengineering,data encryption and image processing and so on.Therefore,it is of great practical significance to combine the memristor with the nonlinear chaotic system to design a better memristor chaotic system.The paper focuses on several new types of memristive chaotic systems based on HP memristor.The basic dynamic analysis and circuit implementation are performed.The chaotic attractors are obtained by the changes of the system parameters and one memristor parameter.Furthermore,the feedback control of a complex chaotic system with perturbation is explored.The main research content is as follows:(1)A memristor is introduced into a three dimensional chaotic system based on the augmented Lü system.This interesting and promising behavior can generate complex single,double and four-scroll chaotic attractors only by varying a parameter.Standard nonlinear diagnostic tools such as equilibrium stability,symmetry,the time domain spectrum,power spectrum and Poincare are employed to investigate its complex dynamic characteristics.The system is simulated by the SPICE circuit.A fully good agreement is observed between Spice simulation results and the theoretical analysis.Subsequently the pulse chaos synchronization is realized from the perspective of the maximum Lyapunov exponent.(2)A novel chaotic system containing a HP memristor model is proposed,and the basic dynamics analysis and circuit simulation verification of the proposed system are carried out.Of particular interest is that the proposed memristive chaotic system can generate multi-scroll attractors and the extended attractors only by varying the system parameter values.And through theoretical derivation and numerical simulation,the time domain wave-forms,power spectrum,Lyapunov exponent are investigated in detail.In addition,the memristive chaotic system has a large chaotic region.It can be seen that the system have rich chaotic characteristics due to the introduction of the memristor,which can be applied to image encryption,secure communication and so on.(3)A four-dimensional fourth time hyper-chaos system containing a memristor has been put forward.The basic dynamics behaviors of the hyper-chaotic system,such as the time domain spectrum,power spectrum,Poincare map,Lyapunov exponent and dimension are investigated in detail.Then,a SPICE-based analog circuit is presented.The method of linear feedback control realizes the synchronization of the memristor hyper-chaos system.(4)Because complex variables can be separated into two components of real and imaginary components,it has more complicated dynamics behavior.Therefore,a new complex chaotic system is proposed based on the Chen system.The dynamic behavior of the proposed complex chaotic system is analyzed in detail.Next,the parameters perturbation and external disturbances are also considered.Therefore,the chaotic synchronization of complex chaotic system is realized under the consideration of the parameters perturbation and the external disturbances.