Center Manifold Analysis For Static Bifurcation And Normal Forms

This paper addresses the dependency of solution of differential equation on initial data andrncontrol parameter. To reduce the dimension of the system, we use center manifold reductionrnmethod. Mainly, the paper focus on the cases of static bifurcations occur and non bifurcation.rnWe transformed the fixed points and control parameter to zero. This greatly helps us to usernlower order approximation of Taylor series. Finally, by using center manifold reduction andrnTaylor series expansion we construct the normal form of such types of bifurcations

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