Numerical computation of stability and detection of Hopf bifurcations of steady state solutions of delay differential equations |
| |
Authors: | Koen Engelborghs Dirk Roose |
| |
Institution: | (1) Department of Computer Science, K.U. Leuven, Celestijnenlaan 200A, B‐3001 Heverlee, Belgium |
| |
Abstract: | The characteristic equation of a system of delay differential equations (DDEs) is a nonlinear equation with infinitely many
zeros. The stability of a steady state solution of such a DDE system is determined by the number of zeros of this equation
with positive real part. We present a numerical algorithm to compute the rightmost, i.e., stability determining, zeros of
the characteristic equation. The algorithm is based on the application of subspace iteration on the time integration operator
of the system or its variational equations. The computed zeros provide insight into the system’s behaviour, can be used for
robust bifurcation detection and for efficient indirect calculation of bifurcation points.
This revised version was published online in June 2006 with corrections to the Cover Date. |
| |
Keywords: | delay differential equations steady state solutions stability 34K20 65J10 |
本文献已被 SpringerLink 等数据库收录! |