Nonlinear Characteristics Of A Class Of Chaotic Circuits And Its Appliications

Compared with the low-dimensional chaotic system,the hyper-chaotic attractors have higher unpredictability,greater randomness,more Lyapunov exponents and key parameters,as well as more complex and changeable topological structures and evolutionary trajectories,so they have reliable security in signal encryption.Nonlinear elements play a key role in the construction of hyper-chaotic circuits and networks.In addition to conventional non-linear resistors,memristor plays an important role in the construction of various kinds of nonlinear circuits because of its memory characteristics as an electronic element with unique memory characteristics,which are widely used to study chaotic circuits,artificial intelligence,programming electronic instruments,secure communication and neural information coding.Based on the development trend and requirements of memristors and hyper-chaotic attractors in mechanical and electronic industry,the emphasis of this paper is to study the dynamic behaviors and state switching characteristics,as well as the modeling,synchronization stability and volt-ampere characteristic curves of of a class of switchable new hyper-chaotic circuits and memristor-based chaotic circuits.The contents include:(1)The existing Lorenz-like equation circuits family consist of five or more operational amplifiers,the circuit structures are complex,unnecessary wiring errors are prone to occur,and the design is not optimized,which are the shortcomings of the existing chaotic circuit technology.In order to solve the above problems,the basic Lorenz chaotic system is improved and the anti-synchronization control of the improved Lorenz chaotic system is studied.Three different control methods are used to achieve the anti-synchronization of the improved Lorenz chaotic system.Based on the improved Lorenz-like chaotic circuit,a third-order Lorenz-like 4+2 chaotic circuit composed of four operational amplifiers and two analog multipliers is proposed to solve the complex structure of the existing Lorenz-like chaotic circuit.(2)In view of the fact that the novel third-order Lorenz-like 4+2 chaotic circuit can only output three chaotic waveforms and three two-dimensional chaotic phase portraits,it can not satisfy some situations in which four chaotic waveforms and six two-dimensional chaotic phase portraits are needed.If we want to output six two-dimensional chaotic phase portraits,it is necessary to increase the circuit structure,which will make the circuit more complex.To solve this problem,on the basis of the new third-order Lorenz-like 4+2 chaotic circuit,a fourth-order Lorenz-like 5+2 hyper-chaotic circuit composed of five operational amplifiers and two analog multipliers is constructed,and the designed hyper-chaotic circuit is optimized and deformed.Thus,a series of corresponding four-dimensional hyper-chaotic circuits with different chaotic attractors are constructed,and its non-linear dynamic characteristics and synchronization stability are also studied in depth.(3)Because the circuit design method of the Lorenz-like hyper-chaotic system still has some limitations,as a result,its performance in engineering application is limited.Specific performance in:it is difficult to improve its frequency response when using analog electronic circuit to realize chaotic oscillator.As a nonlinear device with adjustable and unique memory characteristics,memristor consumes energy without producing energy and does not produce power gain in the circuit.Moreover,it has the advantages of small size and low power consumption,which is especially suitable for high frequency chaotic circuits.Its memory ability of current flowing through the circuit is also not available in conventional chaotic circuit components,so its appearance can significantly promote traditional research.Combining with the physical nonlinearity of memristor,a kind of generalized chaotic circuit with memristor effect is designed by replacing the nonlinearity of a particular kind of chaotic system with memristor function.After dimensionless transformation,the dynamic system is studied with the help of the theoretical analysis of the stability of the equilibrium point of the system and large-scale numerical studies such as Lyapunov exponent,dissipation,chaotic attractors,bifurcation diagram,Poincare section and synchronization control.The defect quantification index of chaotic circuit is proposed to check whether the voltage of all dynamic circuit nodes in the whole circuit is too high to limit the amplitude and to verify whether the chaotic output is consistent with the mathematical model.(4)Because ammeter can measure DC and low-frequency AC current through conductor,but can not measure complex waveform;while oscilloscope can measure complex waveform,but can only measure voltage waveform but not current waveform.For this reason,an active short-circuit line method is proposed for measuring the volt-ampere characteristic curves of various chaotic circuits,especially for the memristor-based chaotic circuits.Aiming at a class of Chua's circuit and a new memristor-based chaotic circuit,the proposed active short-circuit line method is used to successfully measure the volt-ampere characteristic curves of chaotic circuits through circuit simulation experiments and hardware circuit experiments,thus it effectively avoids the situation that the voltage of all dynamic circuit nodes of the whole memristor-based chaotic circuit is too high to limit the amplitude.In addition,in order to find out all kinds of static non-linear function circuits suitable for Chua's circuit with identical parameters,a platform for studying various non-linearities of Chua's circuit is designed based on the constructed memristor-based chaotic circuit,and five kinds of chaotic non-linearities are generated by the active short circuit line method.(5)In view of the weakness of the early fault signal for the mechanical and electrical equipment,and the shortcomings of the traditional detection methods which are difficult to detect,judge and extract accurately,as well as the defects of lacking of optimization and improvement for the existing chaotic secure communication experimental circuit and measurement methods,the large synchronization noise,the unnecessary wiring errors and debugging results in circuit wiring,the proposed new chaotic systems and the designed chaotic circuits are applied to weak signal detection and secure communication circuit.The weak disturbances with weak signals as initial values are input into Lorenz-like chaotic system,hyper-chaotic system and memristor-based chaotic system respectively.Because of the extreme sensitivity of chaotic systems to initial values,chaotic attractor orbits can also change dramatically when they are subj ected to weak disturbances,thus achieving the purpose of detecting weak signals.A new method is proposed to improve the security of transmission signal and the experimental scheme of chaotic modulation secure communication.The comprehensive performance of the circuit is checked by improving the experimental circuit and measurement method.