Modeling,Dynamic Analysis And Circuit Implementation Of Memristor-based Chaotic Systems

As the fourth fundamental circuit element,due to the time-varying and hysteresis properties of real systems and the local nature of integer-order calculus operators,it is difficult to accurately describe the real systems with integer-order calculus models,whereas fractional-order calculus operators have non-local properties.The higher complexity and pseudo-randomness of the chaotic signals generated by fractionalorder memristor chaotic systems make them important for practical applications in areas such as secure communications.This thesis mainly investigates the modeling,dynamics analysis,chaos generation mechanism,and FPGA implementation of the integral-order and fractional-order memristor chaotic systems,and also studies the synchronization of different chaotic systems,which can be summarized as follows.(1)A four-dimensional Colpitts chaotic system is constructed based on a generalized memristor model,a complex dynamics analysis is performed,and the process of the system entering the chaotic state through a period doubling bifurcation,going through period doubling and gradually transitioning from the periodic state to chaotic motion are investigated by combining the power spectrum and phase diagram,and the system passes the NIST test.(2)A generalized memristive model is introduced into the Rucklidge system,and a four-dimensional amnestic chaotic system is proposed.Then,the dynamics of the system is analyzed.Parameter-controlled coexistence bifurcation is discovered,the bifurcation diagram with initial value and the Lyapunov exponential spectrum are plotted to reveal the coexisting attractors of the system,and the extreme multistability of the system is verified by the phase diagram.The dynamics analysis of the system is based on the Hamiltonian energy function.Moreover,the complexity of the system successfully passes the NIST test,and a Multisim-based simulation circuit is built to implement the proposed system,which is also confirmed by the experimental results observed by an FPGA plat form.(3)The dynamical equations of a fractional-order memristive chaotic system are derived based on the four-dimensional Rucklidge memristive chaotic system.The dynamic simulations of the fractional order are carried out using time-frequency domain analysis and the numerical simulations of the fractional order are carried out by means of a prediction correction method.Next,the dynamics of the system is analyzed,and two fractional-order systems with different parameters are synchronised using the non-linear feedback method,and the fractional-order system is synchronised with the integer-order system using the tracking control method,and the complexity of the system passes the NIST test.