Dynamics Analysis And Impulse Synchronization Of Chaos In The Circuit Induced By Time Delay

Chaos phenomenon is random like movement which occurs in a deterministic system.Though chaos has been observed both in numeerical simulation and circuit experiment,there still needs theories to prove that there does exists Chaos in such cases,because the computer simuation has finite precision and observation time of experiment is limited.Therefore,the analysis and judgment of chaos are important issues an circuit systems,and have a more profound scientific significance.In this paper,the topological horse shoe is proven in the chaotic dynamics of direct time delay feedback nonlinear systems.A new chaotic attractor is found in the direct time delay feedback nonlinear systems.In order to better apply these phenominon,a impulse sychronization circuit is designed to implement the chaos synchronization between two chaotic systems both induced by time delay.The main reseanrch dothents are as follows:1)In order to prove that Chen system with directly time-dealy feedback cpmtrol is indeed chaotic,firstly topological horseshoe method is enhanced and the lopological horseshoe in the single attractor is found using the numerical method.According to the topological theory,we prove that the Chen circuil with time delay has topological horseshoes and single-seroll attractors in it is indeed chaotic.This method is simpler and without the need for prior knowledge.2)Secondly,we find that the Chen system with direct time-delay feedback control demonstrates varieties types of attractors according to the the difference parameters of the system,In addition to the simgle-scroll allractor and double-scroll attractors,multi-scroll attractors are observed for the first time in the Chen system with time-delay feedback control and Lorenz system with time-delay feedback control.The dissipation,Lyapunov expotent spectrum and power spectrum are analyzed,and the composite chaotic altractor is observed in circuit experiment.The multi-scroll attractors have greater Lyapunov than the single scroll attractor,which demonstrate a broad application prospect.3)Finally,the time delay Chen system synchronization is considered using the impulse control method.The chaotic circuit with time delay and the impulse circuits are simulated using PSIM software.The circuit platform is build and the synchronization experiment is conducted.The simulation results are consistent with the experimental results by demonstrating chaos synchronization in the single attractor in Chen system with time delay,which prove that the analysis is correct and the method is effective.In this paper,the research on the chaotic dynamics in the Chen system with directly time-delay feedback control is deepen,and the chaos generation mechanisms in the dynamical system with time delay is explored.The methods in this paper provide a reliable theoretical framework for chaos judgment.A new composite chaotic attractor is reported for the first time.The circuit experiment shows the correctness of the design of the synchronization circuit and the theoretical analysis.The time delay circuit demonstrates plenty of dynamical pattern,which will be better engineering application potential.