Coexistence Analysis And Chaotic Synchronization Control Of Non-autonomous Neuron Circuits Based On Memristors

In recent years,thanks to its outstanding characteristics,such as nonlinearity,memory and nanoscale,memristor has attracted wide attentions for the potential applications in pattern recognition,neuromorphic computing,neural networks,and has promoted the development of neuromorphic circuits.At the same time,chaos synchronization control,as a key link in chaos application,has attracted widespread attention in recent years and has quickly become a hot topic.In this thesis,two non-autonomous memristive neuron circuits are constructed,and the rich dynamic behaviors of the two circuits are studied.Next,multi-stable synchronization and memristive coupling synchronization between non-autonomous memristive systems are discussed,and the physical feasibility of the synchronization control method is verified by digital circuit experiments.The main research work is as follows:(1)A non-autonomous FitzHugh-Nahumo circuit with a smooth hyperbolic tangent memristor is designed,and coexistence bifurcation,multistability are analyzed.The tunnel diode in the FitzHugh-Nagumo circuit is replaced by a smooth hyperbolic tangent memristor,and a new type of memristive nonlinear circuit is established.Then,the precise dimensionality reduction model is obtained by the incremental charge-flux method,and the dynamic characteristics are analyzed in the flux-charge domain.The research shows that with the change of the excitation parameters,system parameters and initial value of the system,the dimensionality reduction memristive system exhibits phenomena such as coexistence bifurcation,chaos crisis,and extreme multi-stability.At last,the new research direction of the non-autonomous FHN system was brought about due to the introduction of the memristor.In particular,the Feigenbaum tree aggregation phenomenon was innovatively observed in the memristive FitzHugh-Nagumo system.(2)A FitzHugh-Nahumo circuit containing a hyperbolic tangent memristor and a cubic nonlinear memristor is constructed,and multi-stable,anti-monotonic characteristics are discussed.On the basis of the single memristive FitzHugh-Nagumo neuron system,the third-order charge-controlled memristor is introduced,and the fourth-order double memristive FitzHugh-Nagumo circuit is built.The non-autonomous memristive system depends on the complex dynamic characteristics of excitation parameters,system parameters and initial state,including attractor coexistence characteristics,multi-stable characteristics,anti-monotonic characteristics and various symmetry characteristics,which are analyzed in multiple dimensions through quantitative analysis methods.(3)The synchronization control strategy is designed to realize the multi-stable synchronization and the memristive coupling synchronization of the isomorphic memristive chaotic system,and the digital circuit of the memristive system synchronization based on the FPGA technology platform is completed.Based on sliding mode control and finite time stability theory,a new type of sliding mode controller with smooth function is designed to realize the synchronization of three single memristive FitzHugh-Nagumo systems with different initial values and unknown disturbances.The synchronization of two coupled identical double memristive FitzHugh-Nagumo systems with different motions due to multistablility,unidirectional and bidirectional coupling,is also discussed.The synchronization conditions are derived,and the influences of parameters and initial conditions on synchronous dynamics are analyzed.Finally,the Verilog language and FPGA technology platform are used to complete two kinds of memristive system synchronization digital circuits to verify the effectiveness of the designed controller.