A data-driven algorithm to approximate the Poincaré–Lyapunov constant has been developed
to overcome the tedious calculations involved in the center manifold reduction for
delay-differential equations. By using a single numerical solution at the critical
value of the bifurcation parameter, the flow on the center manifold is recovered by
a least-squares fit. This planar system is then used to compute the Poincaré–Lyapunov
constant. The algorithm is tested for the delayed Liénard equation, the analytic center
manifold reduction forms the basis of the comparison. A performance metric for the
method is defined and computed. Numerical results demonstrate that our method works
well for identifying the Poincaré–Lyapunov constant for delay-differential equations.
