Research On Shape Synchronization Control Of Hyper-chaotic Systems

Chaos is a kind of dynamic behavior that is commonly seen in nonlinear system.Thanks to its ergodicity,sensitivity to initial conditions and pseudo-randomness that similar to stochastic systems,chaotic signal have good frequency characteristics and broadband spectrum what makes it very suitable for secure communication.As the theoretical basis of chaotic secure communication,the drive-response synchronization of chaotic system has been deeply investigated.It is worth noting that there is no uniform definition of the drive-response synchronization of chaotic systems at present,and the control design methods are also diverse.Therefore,it is still of scientific and engineering significance to discuss the new chaotic system drive-response synchronization mode and control strategy.From the view point of the shape of chaotic attractor,this thesis studies the shape synchronization control problem of high-dimensional chaotic system,and designs a secure communication scheme based on high-dimensional chaotic shape synchronization.The main contents of this thesis are as follows:Part ?.The basic theory of chaos as well as the research and application of chaotic synchronization has been briefly introduced in this part.Besides,a short summary of the geometric meaning and the calculation methods of the geometric characteristic variables such as arc length and curvature of plane curve have been.The projection of space curve and the method of reconstructing space curve from the projection of space curve are expounded in detail.Part ?.From the aspect of the shape of the chaotic attractor,the problem of drive-response shape synchronization of four-dimensional chaotic system is studied by means of differential geometry and curve projection method.The main procedure is that projecting the attractor of four-dimensional chaotic onto two-dimensional coordinate plane,and then a set of shape synchronization controllers are designed to make the projection of the response system shares the same shape with the projection of the four-dimensional chaotic drive system.Finally,the state of the four-dimensional chaotic driving system is reconstructed from the state of the response system by using the spatial curve reconstruction method,which completes the task of the whole four-dimensional chaotic system shape synchronization.Compared with the low-dimensional chaotic system,the hyper-chaotic system(dimension > 3)has more positive Lyapunov exponents,which makes the dynamic characteristics of the system more complex and the degree of chaos higher.In addition,the chaotic attractor of hyper-chaotic system is not geometric intuitive,so compared with the existing research results of low-dimensional chaotic system shape synchronization,the research of high-dimensional chaotic system shape synchronization is more difficult.Because of this,it can be predicted in theory that the application of the shape synchronization control method to secure communication will have better security.Part ?.Based on the existing research results on shape synchronization of low-dimensional chaotic systems,a general method of shape synchronization control for n-dimensional hyper-chaotic systems is summarized.