| As an important part of nonlinear science research,chaos is widely involved in the fields of life science,economy and finance,complex neural network,communication security,etc.,which attracts the research interest of many scholars.With the progress of science and technology,chaos synchronization,as the key contents of chaos research,plays an indispensable role in the field of communication security and aerospace automation engineering.Therefore,the study of chaos synchronization control is still a subject worth exploring.The main contribution of this thesis is the findings of a new Kd V-BurgersKuramoto(hereinafter referred to as KBK)chaotic system,together with the explorations of chaotic dynamics and chaotic synchronization control related to the new KBK chaotic system.The specific contents are as follows:1.On the basis of existing literature,this thesis considers adding a nonlinear term into the original KBK equation,then a new class of KBK equation and its equivalent 3-D autonomous system are obtained after the traveling wave transformation.The Lyapunov exponents,Lyapunov dimension and Poincare map of the new system are obtained by using the chaotic analysis method,and sensitive to initial conditions,system dissipation and attractor existence of the new system are explored successively,which verify the chaotic characteristics of the new system from different ways.In addition,the stability of the equilibrium point is analyzed by means of Routh-Hurwitz stability criterion.2.Combined with chaotic characteristics of the new KBK chaotic system,and based on the Lyapunov stability theory,we respectively study the complete synchronization of the new KBK chaotic system with known and unknown parameters,the modified function projective synchronization and the corresponding parameter identification between different KBK chaotic systems,and the modified combination projective synchronization as well as parameter estimation between the new KBK chaotic system and Genesio-Tesi chaotic system by means of the nonlinear feedback control and the adaptive control.Numerical simulations are presented to illustrate the applicability of the theoretical process. |
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