A Perturbation-Incremental Method for Delay Differential Equations

A perturbation-incremental (PI) method is presented for the computation, continuation and bifurcation analysis of periodic solutions of nonlinear systems of delay differential equations (DDEs). Periodic solutions can be calculated to any desired degree of accuracy and their stabilities are determined by the Floquet theory. Branch switching at a period-doubling bifurcation is made simple by the present scheme as a parameter is simply increased from zero to a small positive value so that a solution on the new branch is obtained. Subsequent continuation of an emanating branch is also discussed. The advantage of the PI method lies in its simplicity and ease of implementation.