Design Of Fractional-order Nonlinear Systems Based On Memristor

The number of nonlinear system attractors represents the association and memory ability of the system.Fractional-order nonlinear systems can extend the number of the chaotic attractors,and they have stronger memory ability than integer-order ones.Due to the natural memory ability,memresistor can be used to increase the storage capacity of the nonlinear system.This article is mainly aimed at the construction of nonlinear dynamic system,simulation and the stability analysis,we study the traditional integer-order and fractional-order generalized Lorenz system to fractional Lorenz system deeply,and design a new fractional-order unit circuit,apply it to the heterogeneous circuit simulation.We design a generic memristor whose memristance function polynomial is alterable integral exponents and alterable fractional exponents,study its application in simple chaotic system.This article focuses on:1.A traditional 3-D integer-order Lorenz system is constructed,dynamics analysis are developed,which theoretically confirmed the existence of chaotic attractors.Design the scheme of circuit implement for integer-order system,simulation results confirmed the physical realizability of the system.Simply replace the integer-order derivatives by fractional-order ones.Based on the theory of fractional-order calculus,transfer functions in Laplace domain have been calculated for a set of fractional-orders iq in(0,1)with decrement of 0.025.A novel basic fractional-order unit circuit named “Assemble Type” is designed consulting to the four existing unit circuits.A heterogeneity circuit has been designed and simulation in Multisim confirm the reliability and diversity of circuit design.Finally,we confirm our simulation results using stability analytical method based on two stability theorems and necessary conditions to exhibiting attractors.2.A memristor whose power of function polynomial is intergral exponents is designed and used to the simplest chaotic circuit system.Numerical simulation in Matlab prove the system exist a typical chaotic attractor.The influence of linear parameters on dynamic behaviors is investigated.The scheme of circuit for the intergral exponents memristor has been designed,numerical and circuit simlations show that the designed device meet the three characteristic fingerprints of a memristor,and it is confirmed to be a memristance.Expand the intergral exponents to the fractional exponents,study the existence of chaotic attractors and the influence of linear parameters on dynamic behaviors.Based on the exponential circuit and logarithmic circuit,the power circuit is designed and used to the circuit of memristor with fractional exponents,which has the better effectiveness and universality.Transform the integer-order simple chaotic system based on the memristor to fractional-order system,give simulation using different combinations of fractional orders in Matlab.Theoretical analysis and numerical and circuit simulations show that the fractional-order system and fractional exponential power memristance function have physical realizability and the effectiveness of the circuit design.The research achievements provide a certain theory reference value to the research of nonlinear dynamic system.