TY - JOUR
T1 - Explicit periodic solutions in a model of a relay controller with delay and forcing
AU - Barton, D.A.W.
AU - Krauskopf, B.
AU - Wilson, R.E.
PY - 2005/11
Y1 - 2005/11
N2 - In this paper we use a combination of numerical and analytical methods to find and construct solutions of a cameo model of relay control, formulated as a piecewise-constant delay differential equation (DDE). Numerical solutions of a related equation, where the discontinuities of the original DDE are smoothed out, are used to guide the construction of explicit solutions of the original DDE. On the other hand, the construction of explicit solutions provides starting data for numerical continuation of the smoothed equation. The stability of the explicit solutions can also be inferred from the numerical approach.
AB - In this paper we use a combination of numerical and analytical methods to find and construct solutions of a cameo model of relay control, formulated as a piecewise-constant delay differential equation (DDE). Numerical solutions of a related equation, where the discontinuities of the original DDE are smoothed out, are used to guide the construction of explicit solutions of the original DDE. On the other hand, the construction of explicit solutions provides starting data for numerical continuation of the smoothed equation. The stability of the explicit solutions can also be inferred from the numerical approach.
UR - https://www.scopus.com/pages/publications/26944431952
UR - https://www.scopus.com/inward/citedby.url?scp=26944431952&partnerID=8YFLogxK
U2 - 10.1088/0951-7715/18/6/012
DO - 10.1088/0951-7715/18/6/012
M3 - Article
SN - 0951-7715
VL - 18
SP - 2637
EP - 2656
JO - Nonlinearity
JF - Nonlinearity
IS - 6
ER -
