Study On Spatiotemporal Dynamics Of Time-delayed Coupled Memristor Chaotic Systems And Experiment Simulations

Memristor is a typical nonlinear electronic component.It can widely be used in the fields of integrated circuits,secure communication,large capacity storage,etc.The main research methods for memristors are to construct memristor model theoretically and simulate the physical characteristics of memristors.Because,currently,memristors can only be realized and studied in laboratories.As the electrons or energy tranfort in electronic circuits composing of memristor,the time-delay effects must be concerned,which is important for understanding of the nonlinear dynamics of memristors.In this paper,we mainly focus on the construction of chaotic memristor system being composed of the window function with odd-order polynomials and the pattern formation dynamics in the time-delayed coupled chaotic memristor systems.Firstly,a memristor model being composed of odd-order window function is proposed.The volt-ampere characteristics of the proposed model is similar with the experimental results.Therefore,the chaotic memristor system and time-delayed chaotic memristor system are constructed based on the known chaotic electronic model.The Hopf bifurcation conditions are theoretically analyzed and testified by numerical computations.We also designed the analog simulation circuit of the new time-delayed chaotic model.The simulation results confirm well with the analytical the numerical computations.Secondly,the chaotic synchronizations between two identical time-delayed chaotic memristor systems being coupled with the real-time coupling and time-delayed coupling.The synchronization conditions are theoretically analyzed with LambertW function theory.The electronic circuits of coupling systems are constructed and simulated experimentally.Finally,we construct two-dimensional time-delayed coupled chaotic memritor array with the proposed time-delayed chaotic oscillators.The coupled systems are numerically computed under different conditions including boundary conditions,coupling strength and delay time.The pattern formation phenomena including axisymmetric pattern,double head spiral waves,kinks pattern are found in the coupling arrays.The gradient time-delayed coupling method is proposed to control the breakup circular pattern,which is proved to be effective numerically.