Dynamic Analysis And Synchronization Of Fractional-order Multi-stable Memristor Chaotic Systems

Since HP laboratory realized the first nano memristor hardware in 2008.Locally-active memristor has great application value in the nonlinear domain.The fractional-order memristor has more complex dynamic behaviors than the integer-order memristor.The description of fractional-order memristor is more accurate and closer to reality than that of integer order.The fractional-order memristor chaotic system plays a significant role in secure communication and image encryption for its more complex dynamic characteristics.In this paper,two fractional-order memristors are introduced into chaotic system with hidden dynamics and neural network system respectively,and a series of studies are carried out on the systems.In view of the above discussion,the following two parts are done:(1)At present,most literatures rarely explore the influence of fractional order on the characteristics of quadratic nonlinear memristor,and this part studies the influence of fractional order on the characteristics of quadratic nonlinear memristor.The numerical simulation results show that with the decrease of order,the hysteresis loop loses its original symmetry about the origin.Then introduced the fractional-order memristor into Li&Sprott chaotic system.The dynamics of the system is investigated by drawing the phase diagram,bifurcation diagram and Lyapunov exponent diagram.The results show that the system can produce the coexistence of asymmetric attractors under the changes of the order and parameter.Then the synchronization control experiment of the fractional-order system is executed,and the synchronization result is verified by circuit.Finally,the hardware circuit of fractional memristor chaotic system is realized on bread board,and the chaotic attractor is obtained on oscilloscope,which verifies the physical realizability of the system.(2)Since the locally-active memristor has been well known by world.Most of studies are focused on integer order locally-active memristors.In this paper,a multistable fractional-order local active memristor is constructed.A multi-stable fractional-order locally-active memristor is constructed.The multistability,local activity and nonvolatile characteristics of the locally-active memristor are expounded,and then the locally-active memristor is used to replace the self connected synaptic weight in the fractional-order Hopfield neural network.By studying the effect of the parameter,order and the initial conditions on system dynamics,it is found that there is not only asymmetric coexistence,but also extreme multistability caused by the existence of locally-active memristor.Finally,an analog circuit is built to verify the numerical simulation results.