Research Of Chaotic Systems Based On Memristor And Fractal Structure

Memristor is a fourth basic circuit element with variable resistance,nanoscale size,non-linear characteristics,automatic memory,and low power consumption.The introduction of the memristor into nonlinear chaotic circuits is beneficial for generating complex chaotic signals and improving the complexity of chaotic signals.Therefore,it is of practical significance to design memristor-based chaotic circuits with rich dynamical behaviors.The investigation of chaos and fractal was well established,yet few fractal processes have been applied to chaotic systems to generate complex multi-scroll chaotic attractors.Chaotic systems processed by the fractal algorithm have higher sequence complexity and good randomness,making them more valuable for image encryption,spread spectrum communication,secure communication,and weather prediction.In this dissertation,several chaotic systems with complex dynamical behavior are constructed employing the relationship function between charge and flux of the fluxcontrolled memristor model,and detailed dynamical analysis and circuit implementation are performed.In addition,the combination of the fractal algorithm with memristor-based chaotic systems is also focused on,while generating multi-scroll chaotic attractors with different topologies by constructing different fractal systems.The research work highlighted in this dissertation can be summarized as follows:(1)A memristor-based double-scroll chaotic system is designed.By changing the polarity of the memristor,the upper-lower double-scroll chaotic attractors are observed,and the system can transition from the chaotic state to the periodic state as the corresponding parameter of the memristor is adjusted.In addition,a variety of complex dynamical phenomena such as coexisting attractors,transient phenomena,sustained chaos,bi-stability,and intermittent chaos are observed.Subsequently,the PSPICE circuit simulation and the MCU digital hardware implementation demonstrate the physical existence of the upper-lower double-scroll chaotic attractors.Based on the designed recursive back-stepping controller and the proposed chaotic system,we present a method to detect weak multi-frequency signals embedded in Gaussian noise.Experimental results prove that the proposed method can detect each frequency of a multi-frequency weakly periodic signal submerged in a Gaussian noise background,which is important for promoting the engineering application of the memristor.(2)Two novel twin multi-scroll chaotic systems are designed by inputting different flux variables to the memristor-based on the simplified Chua system.The two systems not only produce multi-scroll chaotic attractors with different topologies but also exhibit a variable number of scrolls.Then the coexisting multi-scroll chaotic attractors are observed.Next,MCU digital hardware experiments verify the chaos generation capability of the twin systems.Finally,an encryption scheme is designed based on the twin chaotic systems and the Arnold mapping matrix.Simulation experiments prove that the algorithm is characterized by large key space,a large amount of information,and robustness,which can effectively resist the attacks of existing methods.(3)A novel memristor-based chaotic system is designed and analyzed.The main advantage of this system is that both multi-scroll chaotic attractors and extended chaotic attractors can be generated by simply adjusting the system parameters.Furthermore,the dynamical phenomena of coexisting multiple multi-scroll chaotic attractors can be found.Next,the system is combined with the classical Julia fractal and the higher-order Julia fractal,respectively,to generate various circular chaotic attractors with controllable scroll numbers.The chaotic attractors of the high-order Julia fractal system are also implemented by employing MCU digital hardware.The phase diagrams shown by the oscilloscope are consistent with the numerical simulation results,proving the correctness of the theoretical analysis and numerical simulation.(4)A double-scroll chaotic system based on the flux-memristor model is proposed,which has a line equilibrium point and two unstable equilibrium points.The chaotic behaviors of the proposed system are confirmed by the analysis of phase diagrams,recurrence diagrams,and instantaneous phases.A new class of multi-scroll attractors,such as multi-scroll circular attractors,separated multi-scroll attractors,and nested multiscroll attractors,is observed employing the fractal algorithm in combination with the proposed memristor-based chaotic system.The spectral entropy complexity(Spectral Entropy,SE)experiments show that the post-fractal sequences have a higher complexity.Considering the point of view of engineering applications,the NIST 800-22 test results demonstrate that the post-fractal sequences have good randomness,which provides a theoretical basis for the next applications in image encryption.Finally,the existence of fractal multi-scroll attractors is verified by a microcontroller MCU hardware platform.