Analysis And Circuit Realization Of Conservative Chaotic System Based On Three-terminal Memristor

As the fourth kind of basic element besides resistance,capacitance and inductance,Memristor model has attracted scholars' attention widely.Its application in the field of chaos has also been extensively studied.The 4D Euler rigid body equation is a strictly conservative nonlinear system.The energy of Hamilton and Casimir and the phase volume of the system are conserved.It can only produce periodic orbit and can not produce more complex dynamic behaviors.Because the Lyapunov dimension of the conservative chaotic system is an integer dimension,the system can traverse any position in the phase space.Compared with the dissipative system,the conservative chaotic system has better pseudo-random characteristics and has certain research value.The research shows that the energy conservation of the 4D Euler rigid body equation can be broken,generating a conservative chaotic system by applying the complex nonlinearity of the three-terminal memristor.The system has higher dimension and stronger randomness and is suitable for engineering fields such as encryption.Therefore,it is necessary to construct the theory and verification of this kind of chaotic system.The main contents of this paper are as follows:(1)Derive the 4-dimensional Euler rigid body equation from the 3-dimensional fixed-point rotating Euler equation.This Euler equation can only produce periodic orbit.This thesis found that the non-strictly conservative chaotic system can be constructed by breaking the energy conservation.Six cases of the system are obtained by different ways of energy destruction,four of which can produce phase-volume conservative chaos.According to the definition of three-terminal memristor,the two-terminal memristor is transformed into a three-terminal model,and the basic properties of the memristor are verified.The memristor model is used to break the energy conservation,and six cases of systems are obtained,four of these are phase volume conservative chaotic systems with three-terminal memristor.Simulation research verifies the correctness of the theory.(2)Aiming at a specific situation in the proposed phase-volume conservative chaotic system with memristor,the equilibrium point characteristics are studied,the conservative characteristics of the system are verified.The generalized Hamilton energy function is used to analyze the relationship between the change of its dynamic behavior and the magnitude of the energy value.The dynamic behavior of the system is analyzed in detail using equilibrium point,Poincare cross-section and Lyapunov exponent.The phase volume conservative chaotic system with super large Lyapunov exponent is obtained by mechanism,which can be applied to secure communication based on chaos.(3)For the proposed conservative chaotic system,Multisim circuit simulation is carried out,and the specific transformation steps of the system are given.The circuit model of a phase volume conservative chaotic system with a three-terminal memristor is built by using real hardware.A simple random sequence generating circuit module is given to transform chaotic signals into random sequences.The experimental results of the analog circuit prove the existence of conservative chaos and the correctness of numerical simulation results.