scholarly journals Generalised Lyapunov-Razumikhin techniques for scalar state-dependent delay differential equations

2020 ◽  
Vol 13 (1) ◽  
pp. 85-104
Author(s):  
F. M. G. Magpantay ◽  
◽  
A. R. Humphries ◽  
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Scalar State ◽  
State Dependent ◽  
State Dependent Delay ◽  
Delay Differential

NUMERICAL BIFURCATION ANALYSIS OF DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

2001 ◽  
Vol 11 (03) ◽  
pp. 737-753 ◽  
Author(s):  
TATYANA LUZYANINA ◽  
KOEN ENGELBORGHS ◽  
DIRK ROOSE
Keyword(s):  
Differential Equations ◽  
Bifurcation Analysis ◽  
Delay Differential Equations ◽  
Constant Delay ◽  
State Dependent ◽  
State Dependent Delay ◽  
Numerical Bifurcation ◽  
Delay Differential ◽  
Steady State Solutions ◽  
Numerical Bifurcation Analysis

In this paper we apply existing numerical methods for bifurcation analysis of delay differential equations with constant delay to equations with state-dependent delay. In particular, we study the computation, continuation and stability analysis of steady state solutions and periodic solutions. We collect the relevant theory and describe open theoretical problems in the context of bifurcation analysis. We present computational results for two examples and compare with analytical results whenever possible.

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