Linear Slowly Varying Bifurcation Of Non-linear Dissipative Systems And Control

This paper is on the basis of usual bifurcation,firstly it deals withtime varying bifurcation of non-linear dissipative systems,what'smore,bifurcation parameter is linear slowly vary along time ,itsstudying method uses center manifold theory,It is shown that the motionof slowly varying bifurcation of high dimensional dissipative systemswith a zero and negative real segment eigenvalue can be approximated bya 1 dimensional dynamical system with a slowly varying bifurcationparameter,and can apply to bifurcation with many zero and negative realsegment eigenvalue. Secondly, it uses a new method of scaling balance ( Haberman usestechniques of matched asymptotic expansions) to study a 1 dimensionalslowly varying bifurcation, and the bifurcation transition values areestimated through the scaling balance,and put forward its shortage, andapply to transition bifurcation. Lastly, this paper investigates the feedback control problem of thetime varying bifurcation equation with incompleteness parameter,through choose bifurcation parameter, System will appear Hopf bifurcation,thereby analyze exeistence and stable of periodical solutions,mostly analyze this problem through two examples , special literature is notinvestigated about this part to this day.