Dynamics Of Chaos In Bose-Einstein Condensate

Chaos is a complex very common phenomenon in nature,and the specific refers to occur in a deterministic system random uncertainty and repetitive motion,in nonlinear systems,chaos is a kind of special movement form,widespread under certain parameter control,the system can be from order to disorder,present the bifurcation,shown as the periodic motion and the periodic motion and chaotic theory is one of the most important achievements in nonlinear science since eighties of the20 th century,the research of chaos at an astonishing speed development,has become a unique concept system of discipline.With the continuous improvement of chaos theory,the research on chaos becomes more and more in-depth,especially the characterization of chaos in nonlinear systems.Chaos in Bose-Einstein condensate(BEC)system has become a hot issue in current research.Under the basis of chaos theory,this paper tells the chaos research status at home and abroad,the characteristics of BEC are analyzed,a numerical analysis method for simple processing,using the Matlab software to Bose-Einstein condensation system is put forward based on the model under the Runge-Kutta method of software simulation,using Fortran programming development environment,and realizes the hardware simulation in this paper the research of chaotic chaos,chaos of characterization problem is that in recent years of the most significant progress in the study of chaotic project from different indicators for chaos said,let the chaos of the research had a more significant value.This paper analyzes the indicators of chaos characterization one by one,analyzes the nature of BEC system and its various chaotic indicators successively,and realizes the chaotic indicator characterization with MATLAB and other software.In the process of studying chaos of BEC system,this paper USES various discriminant methods,such as Poincar?e sections and Power spectra,Lyapunov index and fast Lyapunov index which respectively apply variational method to calculate some chaos discriminant indexes.Chaotic synchronization means that the orbits of one chaotic system converge to the orbits of another chaotic system,and the two systems remain consistent in the following time.Generally speaking,hybrid synchronization refers to the process in which two or more chaotic systems adjust certain dynamic properties to achieve a common behavior under the action of coupling or external forces.Overview of duffing system and BEC is synchronous,and the synchronization between two BEC system,finally introduced the synchronization control of chaos,chaos synchronization control method is introduced,separate the two is the same as using different methods to achieve synchronization between chaotic systems,and then analyze the duffing system and BEC system synchronization,using active control method for synchronization,using Simulink simulation first,the last synchronization on the single chip microcomputer STM32.