Response Analysis at Near Critical Point of Hopf Bifurcation in Nonlinear Systems

Abstract

It is well known that if for a nonlinear system the parameterphas a small change, the multiple non-semi-simple defective eigenvalue can be separated into close eigenvalues, which is known as the near defective eigenvalue. For such a case, although the close eigenvalues are distinct, the system still has bifurcation property in natural. This paper presents the response analysis method at the near critical point of Hopf bifurcation in nonlinear systems. A numerical example is given to illustrate the application of the proposed method.