Design And Circuit Realization Of Chaotic System Based On Equilibrium Point

Chaos is a kind of special non-linear phenomenon which has the characteristics of initial value sensitivity,trajectory pseudo-randomness and self-similarity.It has been widely studied and applied in various important disciplines and production practices.Because the performance requirements of applying chaotic systems in different fields are different,it is particularly important to design a chaotic system that meets the relevant requirements.Many scholars have developed various new methods from different aspects such as nonlinear characteristics,physical characteristics and dynamic characteristics of chaotic systems to generate chaotic systems with different functions,such as multi-wing chaotic system,multi-scroll chaotic system and time-delayed chaotic system.And the use of equilibrium point analysis to study chaotic system is one of the most important analysis methods.Memristor is a component with better nonlinear characteristics.In this paper,the activation function of a new chaotic system based on Liu chaos is replaced by the fluxcontrolled model of memristor.And then a chaotic system is obtained,its equilibrium point and the stability of the equilibrium point have very strong plasticity,and the system phase diagram can be mixed and turned over by changing the parameters.Whereafter,the influence of the parameter change of the chaotic system based on the memristor is analyzed in detail,so as to further analyze the reasons for the changes of the system attractors which caused by the stability changes at the equilibrium point.And,for the first time,the Newton iteration method and FPGA technology are used to design and implement a chaotic system that contains the nonlinear term of the flux-controlled memristor,and the generated chaotic signal is connected to an oscilloscope to generate the corresponding chaotic attractors,thereby verifying the effectiveness and feasibility of the chaotic system in production and application.The equilibrium point and its related characteristics have an important influence on the chaotic system.Therefore,the study of the characteristics of the equilibrium point has a major breakthrough in the design of a new type of chaotic system.Some scholars have used the stability of the equilibrium point to classify and expand it,and proposed new chaotic systems such as multi-scrolls and toroids,and put forwarded corresponding construction methods.In this paper,the influence of the equilibrium point on the structural characteristics of the chaotic system is discussed.The purpose of this paper is to make use of the equilibrium point and its stability to construct a chaotic system that has potential value for actual production.What’s more,a new kind of chaotic system with dual equilibrium point is proposed,which is named dual chaotic system,and it provides another feasible solution for the design of a new chaotic system.In order to explain the dual chaotic system,we first construct two chaotic systems with the same number and position equilibrium points,the mathematical model with the exception of the coefficients and the positive and negative is the same and the stability of all corresponding equilibrium points is opposite.Moreover,propose the concept of the chaotic system with dual equilibrium point,and the chaotic system which satisfies this type is called dual chaotic system.The dynamical characteristics of the dual chaotic system are analyzed in detail.And the dual chaotic system model of the two chaotic systems under different activation functions and multi scroll chaotic systems is proposed.Then we propose a chaotic system relative to the classical Chua and Jerk chaotic system,which has been explored for the application of the dual phenomenon in more chaotic systems.After that,using the nonlinear characteristics of two pairs of anti-parallel diodes as the nonlinear term of the classical dual chaotic system,and using the similarity of the dual mathematical model to design a circuit that simply switches two chaotic systems through switches,and through the oscilloscope to display its waveform.Finally,by changing the structure of the chaotic system and thus affecting the equilibrium point of the system,a method of transforming chaotic system into hyper-chaotic system is proposed,and the new three-dimensional chaotic system,Lorenz chaotic system,and Rossler chaotic system proposed in Chapter 3 are used as examples.Furthermore,the conjecture of the reason that this method can produce hyper-chaos phenomenon is put forwarded,which provides some theoretical ideas and directions for the design and application of chaotic systems.