Several Special Hyperchaotic Complex Systems And Their Synchronization Control

Chaos theory is a research hotspot in the field of nonlinearity.It is widely used in communication,aerospace,biology,military and other fields.In recent years,the study of chaotic systems in complex number domain has attracted the attention of many scholars.Compared with real chaotic systems,complex chaotic systems with state variables in complex domain will have more complex system characteristics and dynamic behavior.For hyperchaotic complex system,it has higher dimensions and more controllable parameters.When applied in communication encryption and other fields,it can greatly enhance the security of communication.Therefore,this thesis constructs several new types of hyperchaotic complex systems,analyzes their system characteristics and attractors,puts forward the concepts of Parametric attractors and chaos family,and realizes the synchronous control of these new types of hyperchaotic complex systems.The main contents and innovations of this thesis are as follows:(1)Construction and characteristic analysis of the first kind of new hyperchaotic complex system.Based on the complex Lorenz chaotic system,the first kind of new hyperchaotic complex system is constructed,the parameters of the system are determined,and the system characteristics are analyzed.Firstly,the nonlinear term and feedback term are introduced into the first dimension of the complex Lorenz chaotic system to construct a more complex system equation.Then,the dimension is further improved to obtain a new hyperchaotic complex system.Then,the real part and imaginary part of the new system are separated and transformed into an equivalent 6-dimensional real chaotic system.The Lyapunov exponent of the system is calculated,the symmetry,dissipation and Poincar ésection of the system are analyzed,the influence of parameter changes on the system is studied,the attractor phase diagram of the new hyperchaotic complex system is observed,and the "0-1" test is carried out.Then,the new hyperchaotic complex system is extended to fractional order and mixed order,the system characteristics of the system under fractional order and mixed order are studied,and the influence of order on the system is discussed.Finally,the mechanical analysis of the new hyperchaotic complex system is carried out.(2)The construction of the second kind of new hyperchaotic complex systems and the proposal of special attractors.Based on the complex Chen chaotic system,the second kind of new hyperchaotic complex system is constructed,the Lyapunov exponents of the system is calculated,the system characteristics are analyzed,and the "0-1" test is carried out.The attractor phase diagram of the new hyperchaotic complex system is observed.It is found that there is a strange chaotic attractor,which is called butterfly-like attractor.The influence of parameter variation on chaotic attractor is systematically studied.It is found that the system will show different attractor forms under different parameter values,which is called parametric attractors phenomenon.The coexistence analysis of the system shows that there is no coexistence attractor in the system.The new hyperchaotic complex system is extended to fractional order and mixed order,the influence of order and parameters under fractional order is discussed,and the mixing degree under mixed order is discussed.It is found that the new hyperchaotic complex system of fractional order and mixed order also has the phenomenon of Parametric attractors.The mechanical analysis of the system is carried out.This thesis summarizes these two kinds of new hyperchaotic complex systems,generalizes them,and puts forward the concept of chaos family.(3)Simulink implementation of two kinds of new hyperchaotic complex systems.Two kinds of new hyperchaotic complex systems are simulated in Simulink,and the same attractor phase diagram as MATLAB simulation is obtained.It is proved that the two kinds of hyperchaotic complex systems are feasible to be realized by actual circuits.(4)Synchronization of two new classes of hyperchaotic complex systems.For the first kind of new hyperchaotic complex system,taking it as the driving system and response system,a complete synchronization controller is designed,and the actual circuit is simulated with Simulink to prove the feasibility of the actual circuit to realize synchronization control.For the second kind of new hyperchaotic complex system,a tracking synchronization controller is designed,which can track constant,sinusoidal function and complex Chen chaotic system,and track the last expected target in a short time.To sum up,this thesis constructs two kinds of hyperchaotic new complex systems,finds the "butterfly-like attractor",puts forward the "parametric attractors",and gives the definition of chaos family.Simulink simulation is proposed to realize the complete synchronization of complex hyperchaotic system,and the tracking synchronization of the second kind of new complex hyperchaotic system is realized.