Dynamic Research And Circuit Realization Of Several Types Of Hyperchaotic Systems

Since 1971,Leon O.Chua first proposed the concept of memristor and proved it,the traditional circuit theory have been developed for decades.The memristor is a passive nano-information device with memory characteristics.It plays a huge role in non-volatile memory element manufacturing,artificial neural networks,nonlinear circuits and other branches.In nonlinear circuit science,people insert memristors into known chaotic circuits,which can often produce more complex chaotic characteristics,and even convert chaotic systems into hyperchaotic systems.Hyperchaotic systems play a huge role in secure communication,image encryption,signal noise reduction,etc.due to their higher dimensionality and more complex topology.Based on this,it is necessary to conduct an in-depth discussion on hyperchaotic systems based on memristors.This paper uses the method based on state variable feedback,the feedback method based on memristive realization,and the method of replacing the original circuit resistance based on memristive to design three different new hyperchaotic systems.After using a series of qualitative and quantitative methods to carry out detailed dynamic analysis and numerical simulation analysis of the hyperchaotic system,and to further determine the chaotic characteristics of the system,this paper builds the corresponding circuit model according to the state equation of each system,and Simulink simulation verification was performed on the built circuit,which proved the effectiveness of the circuit implementation.This paper provides a certain reference value for the design and realization of hyperchaotic circuits.The first chapter introduces the research background and significance of this article,and respectively launches a description of the current research status at home and abroad on memristors,chaotic systems,and hyperchaotic systems.The end of the chapter briefly explains the main work done in this article and the structure of the article.The second chapter focuses on chaotic systems and hyperchaotic systems,and introduces the definition,characteristics,qualitative and quantitative research methods of chaotic systems and hyperchaotic systems in turn.Chapter Three uses the method based on state variable feedback to construct a new four-dimensional hyperchaotic system.The chaotic characteristics of the system are qualitatively analyzed using basic dynamic analysis methods such as the stability analysis of the equilibrium point and the phase trajectory diagram of the attractor.Numerical simulation methods such as the Lyapunov exponential spectrum and the Poincaré diagram are used to analyze the chaotic characteristics of the system.Quantitative analysis finally confirmed that the four-dimensional dynamics system has hyperchaotic behavior in a specific interval.The corresponding circuit diagram of the system was built,and the built circuit was simulated in Simulink to verify the accuracy of the circuit implementation.In Chapter 4,a new four-dimensional memristive hyperchaotic system is constructed using the state variable feedback method based on the memristor.Using qualitative and quantitative analysis methods,it is determined that the four-dimensional dynamics system has hyperchaotic behavior.the circuit corresponding to the hyperchaotic system is built using the method of modular design and the corresponding circuit model is established in Simulink,and the image output by the oscilloscope is established Compared with the image output by Matlab,the results are consistent,verifying the real validity of the circuit implementation.In Chapter 5,a new four-dimensional memristive hyperchaotic system is constructed by replacing the resistance of the original chaotic circuit with a memristor.Different from the method of directly introducing the memristive model into the differential equation used in Chapter 4,this chapter replaces the resistance in the original Lü system circuit with the memristor components in turn,thus obtaining several new fourdimensional hyperchaotic systems.The characteristics are summarized.