Locally-active Memristors And Their Complex Dynamics Analysis And Applications

Memristor is a kind of nonlinear resistor with memory,which has important potential applications in new generation of non-volatile memory,nonlinear circuits,artificial neural networks and logical operations.In 2005,Chua proposed that local activity is the origin of complexity,and then defined the concept of locally-active memristors.Memristors can be divided into locally-passive memristors,which can simulate synaptic properties,and locally-active memristor,which can simulate the function of neurons.Only in locally-active regions complex and rich dynamic behaviors can be generated,and it is found that the neural network working under edge of chaos mechanism can improve computing capacity and optimize neural computation.Memristive neural network can break Von Neumann architecture and establish a new integrated computing system.Non-volatile locally-active memristors can play the role of chaos-memory-computation at the same time,since the modeling of locally-active memristors and exploration of their complexity mechanism are of great significance.In this thesis,two novel models of locally-active memristor are proposed,their complex dynamic characteristics are studied,and they are applied to image encryption.The main innovative works are as follows:(1)A binary voltage-controlled locally-active memristor is designed,whose non-volatility and locally-active regions are analyzed by using POP and DC V-I plot.The operating point Q in locally-active regions was selected for linearization analysis by using small-signal equivalent circuit method,and then the zero and pole plot,edge of chaos domain and Hopf bifurcation point at operating points of the memristor were obtained.Finally,two-dimensional oscillating circuit was used for verifying that the circuit can oscillate only in the locally-active regions of memristor,indicating that the local activity is the origin of complexity.(2)A Tristable locally-active memristor with three stable equilibrium points is designed,whose non-volatile property,locally-active regions and edge of chaos are given.A small signal equivalent circuit at a locally-active operating point is established.Based on the admittance function of the small-signal equivalent circuit,the parasitic capacitance and the parasitic oscillating frequency of memristor are determined.The dynamics of parasitic oscillating circuit are analyzed by Hopf bifurcation theory.Furthermore,by adding an inductor to periodic parasitic circuit,we derive a simple chaotic circuit,whose basic properties and coexisting dynamics are analyzed in detail.We found that it is the locally-active memristor that provides the energy for the circuit to excite and maintain the periodic and chaotic oscillations.(3)A chaotic image encryption system based on Matlab is designed based on chaotic sequence generated by chaotic oscillating circuit of the tristable locally-active memristor,and the sequence generated by the chaotic system is used as secret key sequence to encrypt and decrypt the image selected by user.The encryption system can run on the Windows system to improve the security of image information.