BIFURCATION ANALYSIS IN A GENERALIZED FRICTION MODEL WITH TIME-DELAYED FEEDBACK

In this paper,we consider a generalized model of the two friction models,both of which have two different types of control forces with time-delayed feedback proposed by Ashesh Sara et al.By taking the time delay as the bifurcation parameter,we discuss the local stability of the Hopf bifurcations.Under some condition,the generalized model harbors a phenomenon that the equilibrium may undergo finite switches from stability to instability to stability and finally become unstable.By applying the method introduced by Faria and Magalhaes,we compute the normal form on the center manifold to determine the direction and stability of the Hopf bifurcations.Numerical simulations are carried out and more than one periodic solutions may exist according to the bifurcation diagram given by BIFTOOL.Finally a brief conclusion is presented.