COMPUTING FLOQUET MULTIPLIERS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS

Abstract

Floquet multipliers determine the local asymptotic stability of a periodic solution and, in the context of parameter dependence, determine also its bifurcations. This paper deals with numerical aspects of the computation of the Floquet multipliers for three classes of functional differential equations: ordinary differential equations (ODEs), differential equations with constant delay (DDEs) and differential equations with state-dependent delay (sd-DDEs). Using a collocation approach for computing periodic solutions, we obtain an approximation of the (corresponding) monodromy operator, a monodromy matrix. The eigenvalues of this matrix form an approximation to the Floquet multipliers. The accuracy of the computed multipliers is an important issue in bifurcation analysis of a dynamical system. As far as we know, no prior work on the study of the convergence and accuracy of computed Floquet multipliers for DDEs and sd-DDEs exists. We analyze the dependency of the accuracy of the computed multipliers on the parameters and on the type of collocation approximation. In particular, we show that the accuracy of the computed trivial multiplier is not always comparable to the accuracy of the computed periodic solution and the accuracy of the other computed multipliers.