Bifurcation And Control Of Random Time Delay Complex Networks

In various fields,complex networks have been the hotspot of research in recent years.The wide adaptability of networks has been fully developed in various disciplines,and its dynamic behavior analysis and time delay behavior control have also become the focus of research.Regarding complex networks,various complex models are usually represented by nonlinear systems.In this paper,we investigate the dynamics of complex networks based on the hyper chaotic network model,the Liu system model,the laser complex system and the Sprott B chaotic system model with time delay control.Random,power exponential and magnetron memristor terms are also considered to delve into the more complex behaviour of chaotic systems,and simulations are carried out to obtain waveform diagram,phase plots and bifurcation diagrams of the system to show its dynamics.1.Based on the hyper chaotic complex system adding the time delay control term,the hyper chaotic system time delay control network model is established.The dynamic behavior of the system is analyzed,and the characteristic polynomial of the linearized system is used to analyze the distribution of the root of the characteristic equation for the equilibrium point of the hyper chaotic system.At the same time,the theoretical verification of the Hopf bifurcation near the equilibrium point is given.By controlling the time delay value and parameters,the impact on the system is observed,and Matlab simulation is used to verify the theoretical results.Keeping other coefficients unchanged,the system is locally asymptotically stable at the equilibrium point whent???_<sup>0;the chaotic behavior appears again,and the state of the attractor changes when???_<sup>0.Consider random term and study their effects on low-dimensional chaotic systems.At the same time,further simulate the system.Extend it to the high-dimensional controlled model and explore the effect of adding nonlinear factors such as random terms to high dimensional time delayed models.2.Based on the Liu chaotic system,we study the dynamical behavior of the system,analyse the distribution of its characteristic roots after linearization and give the critical values of its bifurcation parameters,and simulate to verify the correctness of the conclusions.Based on the Liu chaotic system containing power exponential terms,we study its chaotic dynamical behavior and analyse the influence of its relevant parameters on the system.After adding random items,the results are compared,and it is found through the bifurcation diagram that small disturbances do not affect the chaotic behavior.The chaotic system is modelled by considering the magnetron memristor term,and the characteristics of its chaotic system model are analysed to obtain special chaotic phenomena such as biplane attractor rotation and continuous chaos.3.Based on laser complex parametric chaotic systems and Sprott B complex chaotic systems,the time delay control behaviour of real and complex variable parameters is investigated.The distribution of the characteristic roots is analysed by linearising the system and the attractor behaviour and chaotic behaviour changes are studied in conjunction with different control behaviours.Specific examples are given to simulate the dynamical behaviour under different time delay control.