The Research And Application Of Memristor-based Chaotic Circuit

As a fourth basic circuit element,other than resistors,capacitors,and inductors,memristor fills the gap in the relationship between charge and flux.Memristor is a nonlinear resistance with memory function,because of its high speed,low power consumption,nano structure,extensibility,non-volatile and other characteristics,it has potential applications in areas such as nonvolatile storage,intelligent computer system,artificial neural network,and chaotic circuit design.In recent years,in the field of nonlinear circuits and systems,the generation of chaotic attractors and hyperchaotic attractors with complex dynamic characteristics is always hot topic.The memristor open a new window for chaotic system design,as a kind of nano device with nonlinear characteristics,which is used in the chaotic circuit design,and it is advantageous to generate chaotic signal with complex dynamic characteristics.Chaotic signal with complex dynamic characteristics has a potential application in the field of secure communications and image encryption,so design and feature analysis of chaotic circuit based on memristor have received extensive attention of scholars.In this dissertation,the applications of memristor in chaotic circuits are studied,and theoretical analysis,numerical simulation and hardware design are implemented.The main contributions and innovations of this dissertation are summarized as follows:?1?To obtain more complex dynamic characteristics,a method is prop osed to construct memristor-based multi-wing hyperchaotic attractor.The method is simple and universal.By replaceing the resistor with a flux-control memristor in multi-wing chaotic system?Taking the modified multi-wing Lüsystem as example?,the proposed memristive multi-wing system has good hyperchaotic multi-wing features.In addition,we also analyzed the dynamic characteristics of the new system by using phase diagrams,Lyapunov Exponent,Poincare section and bifurcation diagrams for other positions that might be replaced.Based on the above analysis,the steps of constructing the memristive multi-wing hyperchaotic system are summarized.At the same time,we also used discrete components to complete the hardware design and experiment,and the experimental results and simulation results are largely consistent,further verify the validity and complexity of the proposed system.?2?The chaotic system with hidden attractor has some advantages in the field of secure communication and image encryption because of its better hiding and randomness.Therefore,a method for constructing memristive multi-wing hyperchaotic systems with hidden attractors is proposed.A flux-control memristor is added into this multi-wing chaotic circuit.The new multi-wing system not only has hidden attractor?Attractor with no equilibrium point is a special case of hidden attractor.?,but also shows hyperchaotic attractor.Contrapose the different connection ways of memristor,we use Lyapunov Exponent and phase diagram to characterize the hyperchaos and multi-wing characteristics respectively.Finally,it is proved that the proposed memristive multi-wing hyperchaotic system with non-equilibrium is correct by hardware experiment.?3?A four-wing chaotic circuit based on memristor is proposed,which not only produces hyperchaotic attractors,but also presents the characteristics of variable wings.Just adjusting the coefficient of item containing memristor,the proposed memristive four-wing chaotic system can produce the two-wing,three-wing and four-wing attractors,and has complex dynamic characteristics,such as the coexistence of multiple chaotic attractor,transient chaos and state transformation.Moreover,the correctness of the proposed system is proved by theoretical analysis,numerical simulation and hardware experiment.?4?A simple four-order memristive Twin-T oscillator is proposed,and its rich dynamical behaviors can be triggered in the dynamical system.The most striking feature is that this system has various periodic orbits and various chaotic attractors by adjusting Resistor R₂?parameter b?.At the same time,coexisting attractors,Riddled basin and antimonotonicity?Especially,two full Feigenbaum remerging trees in series are observed in autonomous chaotic systems.?are also detected,and their dynamical features are analyzed by phase portraits,Lyapunov Exponent,bifurcation diagram and basin of attraction.Moreover,hardware experiments on a breadboard are carried out.Experimental measurements are accord with the simulation results.At last,we have developed a multi-channel random bit generator,and the generated random sequences are used for simple image encryption.Numerical results illustrate the usefulness of the random bit generator.