Nonlinear Model Construction And Circuit Simulation Of Smooth Flux-controlled Memristor

As two new discoveries in the field of nonlinear science,memristor and cellular neural networks(CNN)have been the focus of research in this field successively.In essence,the memristor is a class of nonlinear resistor with relatively strong memory capacity and CNN is a kind of nonlinear system with relatively strong automatic associative memory capacity,the memory capacity of the new nonlinear systems that combine the two is likely to be enhanced.The main research content of this paper includes designing a new type of smooth flux-controlled memristor,which is combined with CNN properly.And analysis of the dynamic characteristics of the new-type smooth flux-controlled memristive CNNs,the corresponding nonlinear circuit is built for simulation validation.At the same time,a nonlinear system based on memristor which can generate hidden chaotic attractors is constructed.After detailed analysis of the specific dynamics behavior of the system,the feasibility of its application in physical circuit is verified.The core work of this study is as follows:(1)A new traditional four-dimensional CNN capable of generating chaos is designed.In the meantime,a smooth continuous flux-controlled memristor model is defined to replace the piecewise linear function as the output module of the traditional four-dimensional CNN.By adding two cells to generate flux-controlled memristor,in this way,a new six-dimensional smooth flux-controlled memristive CNNs can also producing chaos is constructed.In order to verify the validity and feasibility of this scheme,we use the general electronic components to construct the memristive module and applied it to the whole circuit of the system.Multisim circuit simulation software results shown that the proposed memristive module with the feature of pinched hysteresis loop as well,and oscilloscope display circuit output curves are approximately in agreement with those of MATLAB numerical calculation results within the range of the permitted errors.(2)The circuit diagram of Sprott B chaotic system is constructed,and one of the resistors is replaced by a memristor in it,then a new memristive nonlinear system is obtained again.The system is invariant because it symmetry about the z-axis.It is found that the system is extremely sensitive to the internal parameters of memristor,namely,to change the internal parameters of the memristor,it can produce coexisting chaotic attractors,coexisting period 4 limit cycle,coexisting period 2 limit cycle and coexisting single limit cycle and other hidden chaotic attractors.By comparing its numerical simulation and circuit simulation,it is found that the system can be realized in actual physical circuit as well.In conclusion,the research results of this paper will have some reference value and significance to the traditional nonlinear system,and the discovery of hidden attractor will provide a new direction for further research in the future.