Study On Memory Elements Simulink Modelling And Their Application In Chaotic Circuits

In 1971,professor Chua first proposed the concept of the memristor to characterize the relationship between charge and magnetic flux.With a series of breakthrough research results of modern nanoscience and technology,in 2008,the scientists of HP Labs successfully realized the physical components of the memristor for the first time,and set off a research frenzy of memristors in the world.In 2009,the introduction of two new types of memory components(recalling memcapacitor and meminductor)has attracted wide attention in the industry.Besides the memory characteristics,they behave as nonlinear capacitance and nonlinear inductance at low frequencies,and exhibit linear capacitance and linear inductance at very high frequencies,which motivates them become a research hotspot rapidly.However,two new components have not been physically realized yet.In this paper,under the premise that the memory components are not marketable,the memristor,memcapacitor and meminductor piecewise linear model based on Simulink are built separately.At the same time,Simulink is used to model other models of memory components(such as cubic models),and on the basis of this,the exponential chaotic system based on memristor,chaotic oscillator based on memcapacitor,hyperchaotic oscillator based on memcapacitor and meminductor are constructed respectively.The circuit characteristics of each system are discussed.especially the chaotic dynamics.In addition,the effectiveness of this systems was further verified by Simulink simulation and DSP experiments.The research contents of this paper are as follows:(1)The Simulink models of the memory elements are established on the premise that the memory element has not been marketed.Firstly,according to the general definition of memory components,the piecewise linear mathematical model of the meminductor is designed.Secondly,according to the mathematical models of memristor,memcapacitor and meminductor,the Simulink model which visually reflects their memory characteristics are constructed,that is,the equivalent values of them are associated with their historical state.Also the circuit characteristics of the model are discussed and verified.(2)In order to study the chaotic system which is made up of the classical system,the nonlinear term and memory elements,by adding exponential terms and memristor to the Lii system,the dimension of the original system is increased,and a new chaotic system is constructed.The dynamic characteristics of the system are analyzed.In particular,the role of voltage temperature equivalent Uj in the circuit is discussed.Finally,the system is implemented by Simulink simulation and DSP simulation experiments.(3)The Simulink model of smooth cubic memcapacitor is established.On this basis,a new chaotic oscillator based on memcapacitor is constructed.At the same time,by analyzing the dynamic characteristics of the system in depth,the law of the influence of the initial values and parameters of the system on its system state is obtained.Finally,the effectiveness of the chaotic oscillator is verified by Simulink simulation.(4)In order to study the oscillation circuit containing both the memcapacitor and the meminductor,the non-volatile characteristics of the third-order memcapacitor model and the second-order meminductor model are first discussed by the POP(Power-Off Plot)method(acronym for Power-Off Plot).On this basis,the hyperchaotic oscillating circuit based on memcapacitor and meminductor is constructed.Through analysis,the characteristics of coexisting attractor and infinite equilibrium points are found.Finally,the oscillating circuit is realized by Simulink simulation and DSP simulation experiments.