Discrete-delay Implementation of Distributed Delay in Control Laws

2006 ◽  
pp. 173-194
Keyword(s):  
Distributed Delay ◽  
Discrete Delay ◽  
Control Laws

scholarly journals Discrete delay, distributed delay and stability switches

1982 ◽  
Vol 86 (2) ◽  
pp. 592-627 ◽  
Author(s):  
Kenneth L Cooke ◽  
Zvi Grossman
Keyword(s):  
Distributed Delay ◽  
Discrete Delay ◽  
Stability Switches

scholarly journals On the approximation of distributed-delay control laws

2004 ◽  
Vol 51 (5) ◽  
pp. 331-342 ◽  
Author(s):  
Leonid Mirkin
Keyword(s):  
Distributed Delay ◽  
Control Laws ◽  
Delay Control

scholarly journals Dynamical Behavior and Stability Analysis in a Stage-Structured Prey Predator Model with Discrete Delay and Distributed Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Chao Liu ◽  
Qingling Zhang
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Local Stability ◽  
Dynamical Behavior ◽  
Distributed Delay ◽  
Stable Limit ◽  
Discrete Delay ◽  
Normal Form Theory ◽  
Interior Equilibrium ◽  
Predator Model

We propose a prey predator model with stage structure for prey. A discrete delay and a distributed delay for predator described by an integral with a strong delay kernel are also considered. Existence of two feasible boundary equilibria and a unique interior equilibrium are analytically investigated. By analyzing associated characteristic equation, local stability analysis of boundary equilibrium and interior equilibrium is discussed, respectively. It reveals that interior equilibrium is locally stable when discrete delay is less than a critical value. According to Hopf bifurcation theorem for functional differential equations, it can be found that model undergoes Hopf bifurcation around the interior equilibrium when local stability switch occurs and corresponding stable limit cycle is observed. Furthermore, directions of Hopf bifurcation and stability of the bifurcating periodic solutions are studied based on normal form theory and center manifold theorem. Numerical simulations are carried out to show consistency with theoretical analysis.

BIOLOGICAL DELAY SYSTEMS AND THE MIKHAILOV CRITERION OF STABILITY

2004 ◽  
Vol 12 (01) ◽  
pp. 45-60 ◽  
Author(s):  
URSZULA FORYŚ
Keyword(s):  
Stability Analysis ◽  
Distributed Delay ◽  
Integral Form ◽  
Logistic Equation ◽  
Delay Systems ◽  
Discrete Delay ◽  
Stability Regions ◽  
The Stability ◽  
Delay Logistic Equation

This paper deals with the stability analysis of biological delay systems. The Mikhailov criterion of stability is presented (and proved in the Appendix) for the case of discrete delay and distributed delay (i.e., delay in integral form). This criterion is used to check stability regions for some well-known equations, especially for the delay logistic equation and other equations with one discrete delay which appear in many applications. Some illustrations of the behavior of Mikhailov hodograph are shown.

Sign in / Sign up

Export Citation Format

Share Document