2009/09/22 by Jean‐Philippe Lessard, Lessard, Jean-Philippe
Engineering · Computer Science · Medicine · #Stability and Controllability of Differential Equations #Nonlinear Dynamics and Pattern Formation #Mathematical and Theoretical Epidemiology and Ecology Models
paper · pdf · doi:10.48550/arxiv.0909.4107
An old conjecture in delay equations states that Wright's equation y'(t)= - αy(t-1) [ 1+y(t)], α∈ ℝ has a unique slowly oscillating periodic solution (SOPS) for every parameter value α>π/2. We reformulate this conjecture and we use a method called validated continuation to rigorously compute a global continuous branch of SOPS of Wright's equation. Using this method, we show that a part of this branch does not have any fold point nor does it undergo any secondary bifurcation, partially answering the new reformulated conjecture.