| Memristor is the fourth type of basic circuit element with memory and nonlinearity.It has advantages of rapidity,low power consumption,strong scalability,nanostructure and non-volatility.Therefore,it has a wide range of applications in the fields of memory,artificial intelligence,neural networks and nonlinear chaotic circuits.Designing nonlinear chaotic circuits based on memristors and analyzing the complex dynamic behaviors have gradually become a hot topic in academic research.The non-linear characteristics of the memristor combined with the chaotic circuit can generate a complex chaotic signal,which has applying value in the field of secure communication.In this thesis,two sets of chaotic oscillation systems are constructed with different memristors,and the characteristic of two circuits are analyzed through numerical simulation.After that,the proposed circuits are realized by digital and analog circuit technology.At the same time,the system is applied to digital image encryption.The main research work and innovations are summarized as follows:(1)A Shinriki oscillator with two flux-controlled memristors is designed,and the special symmetry behavior and the reconstruction of extreme multistable phenomenon are studied.First of all,two flux-controlled memristors are introduced into the classic Shinriki oscillator,and a fifth-order mathematical model of the system is established.Next,the stability of the system is judged by analyzing the type of surface equilibrium points.Then,by using dynamic analysing methods such as phase trajectory diagram,Poincaré map,bifurcation diagram,Lyapunov exponential spectrum and basin of attraction,the symmetry behavior affected by specific parameters is studied in the voltage-current domain.At last,with the flux-charge analysis method,the dimensional reduction model in the flux-charge domain is obtained,and the extreme multistable phenomenon of the oscillator depending on the different initial conditions is reconstructed.Meanwhile,the behavior of Bursting in the autonomous system is observed.(2)A dual memristive Shinriki oscillation with generalized memristor is construted.Besides,the equivalent model of memristors are realized,and the nonlinear dynamic behavior of the system is studied.Firstly,the absolute memristor and generalized memristor are equivalently modeled,and their basic characteristics are analyzed.Secondly,the two kinds of memristors are added to the Shinriki oscillator to construct a new memristive chaotic system with line equilibrium points.The chaotic state judgement and equilibrium point stability analysis are realized through 0-1 test and Jacobian matrix respectively.Finally,starting from the static component,the memristive parameter and the dynamic component,complex phenomenon of the oscillator is discussed,including coexistence and bifurcation of multiple modes,antimonotonicity in parameter domain and initial value domain,asymmetry coexistence,and multistability with initial value-dependent.(3)A circuit implementation scheme of memristive chaotic system is proposed,and the chaotic sequence generated by the system is applied to image encryption.To begin with,the memristive chaotic digital circuit in the voltage-current domain is realized based on FPGA technology,the circuit module is described by the Verilog hardware language,and the correctness of the numerical simulation is verified through the different attractor trajectories captured by the oscilloscope.Subsequently,the Multisim simulating software is used to modularly build a reduced-dimensional third-order model,and use five DC voltage sources with equivalent initial values to achieve rapid control of extreme multi-stable phenomena.Finally,a digital image cryptographic system based on the memristive oscillator is proposed,and the reliability and security of the constructed memristive cryptographic system are analyzed through the statistical properties of the ciphertext and the key sensitivity. |
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