David A W Barton et al 2005 Nonlinearity 18 2637 doi:10.1088/0951-7715/18/6/012
David A W Barton, Bernd Krauskopf and R Eddie Wilson
Show affiliationsRecommended by M P Brenner
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.
02.30.Hq Ordinary differential equations
02.60.Lj Ordinary and partial differential equations; boundary value problems
Issue 6 (November 2005)
Received 22 October 2004, in final form 8 August 2005
Published 16 September 2005
David A W Barton et al 2005 Nonlinearity 18 2637
Paivi Simonen et al 1997 Physiol. Meas. 18 155
Sanjeev S Seahra and Paul S Wesson 2003 Class. Quantum Grav. 20 1321
Theodore W Burkhardt 1997 J. Phys. A: Math. Gen. 30 L167
Stephen O'Dell 2006 Inverse Problems 22 1579
B Verma et al 1980 J. Phys. D: Appl. Phys. 13 1605
S Y Tong and Huasheng Wu 2002 J. Phys.: Condens. Matter 14 1231
K Hoshino and M Watabe 1978 J. Phys. C: Solid State Phys. 11 1381
I S Heng et al 2002 Class. Quantum Grav. 19 1889
Yu Zhang et al 2003 Inverse Problems 19 1113