| This thesis conducts a system research on the stability and bifurcation of the nonlin-ear dynamic system by means of recurrence plot,basing on the analysis of the stability and bifurcation of nonlinear dynamical systems.What's more,to partition the phase space easily,symbolic recurrence plot that is referenced in this article.The thesis is composed of three chapters and organized as follows:In the first chapter,we mainly introduce the background and meaning of topic selec-tion,the research background and current situation of recurrence plot and the research content of this article.We introduce two kinds of research methods:recurrence plot(RP)and symbol recurrence plot(SRP),then take rossler system as examples to illus-trate that,symbol recurrence plot can transform recurrence point to recurrence domains successfully.In the second chapter,we introduce the application of recurrence plots to analysis stability of the planar system.Firstly,by analyzing RP,a series of non-linear char-acteristics,including the sink,source and Hopf bifurcation,the effectiveness of the RP method is proved by theoretical analysis and numerical simulation.In the following,the phase space is partitioned successfully by SRP.The stability of equilibrium point in the Lotka-Volterra competition model of the species was studied by SRP in the end.In the third chapter,a kinds of the dynamic behavior of the three-dimensional energy demand-supply system was researched including the staility analysis of the equilibriumpoint,the bifurcation analysis,the global dynamic behavior of the solution of this system,etc.What's more,based on the domestic and international research,this article gives the recurrence plot and symbol recurrence plot of the energy demand-sulpply system which generated sink,source and Hopf bifurcation.providig relatively reliable preference for judging type structure of time-series data and to partition the phase space So.this study has important theoretical and practical significance. |
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