Recent advances about the uniqueness of the slowly oscillating periodic solutions of Wright's equation
By Jean-Philippe Lessard. 2009
62 citations recorded by the source corpus.
Abstract An old conjecture in delay equations states that Wright's equation y ′ ( t ) = − α y ( 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, partially answering the new reformulated conjecture.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/e92e20956ab7af140429ecce923a426cfc539183
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Computational Theory and Mathematics
In Control and Systems Engineering
Citations in the corpus
- Analytic estimates and rigorous continuation for equilibria of higher-dimensional PDEs (2010, methodology): “In [9, 10, 11], validated continuation was adapted to compute global smooth branches of time periodic solutions of delay differential equations and ordinary differential equations.”