Study On Generalized Synchronization Of Chaos In One Class Of Chaotic Systems

Different discipline fields have obtained rapid development since the birth of chaos, especially in the field of biology where has a wide range of applications. The great values and good prospects of chaos synchronization in engineering and technology,military and other areas have been a hot spot of non-linear science in recent years. The complete synchronization as well as generalized synchronization in three species food chain model is studied in this paper, the main works and achievements are as follows:Simply to describe the development of the chaotic, briefly to introduce the three species food chain model in biology and the concept of chaos synchronization between species and the relationship among the species,we introduce the main classifications of chaos synchronization and the mathematic theories and methods used in the monographs and papers,mainly describe the significance of chaos synchronization and generalized synchronization in biology.Three-Species Food Chain Model is a dynamical equation based on a study of the fish culture industry, which studies the food competition of three variables between the same species. It is a foundation that researches the relationship between the different species in the whole ecological chain. Synchronization among the species refers to the phenomenon that the same two species of two different places (or different species) in the same fish pond. Some control method can make the variables of food chain system increase or reduce simultaneously, and the relationship of food competition among species is illustrated from the synchronization between the two food chain systems.(CS).Complete synchronization means that when the time variable tends to infinity, the trace distance with two different initial values between the same two chaotic systems tends to zero. The method of linearly and bidirectionally coupled are used in this paper to get the synchronization between variables of the same two food chain systems.(GS). Generalized synchronization refers to:when the time variable tends to infinity, there is a mapping relationship between traces of two different chaotic systems.In this paper, the method of linearly coupled is used to get the generalized synchronization between the variables of two different food chain systems.The three food chain model is given in this article to study, the boundedness of the three species food chain and its coupler system were proved to be effective based on the Comparison theorem. And we study the synchronization problem with two different initial conditions between the same two food chain chaotic systems. The global synchronization is attained from the theory of time-varying systems and linear coupler between two food chain systems ,and the noise on the impact of biological population and its synchronization were discussed in this paper.We study the generalized synchronization problem between two different food chain chaotic systems. The theorem of generalized synchronization is attained from Lyapunov theory and linear coupler between two food chain systems. After a lot of numerical simulation experiments, we give the corresponding numerical results to verify the correctness of the theoretical methods and effectiveness in this dissertation. Synchronization and generalized synchronization are realized between the various variables of two food chain chaotic systems, we analyse the realationship of food competition among species in the food chain and explain its biological significance.