New Results for Studying a Certain Class of Nonlinear Delay Differential Systems

2010 ◽  
Vol 55 (7) ◽  
pp. 1641-1645 ◽  
Author(s):  
Daoyi Xu ◽  
Liguang Xu
Keyword(s):  
Differential Systems ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Nonlinear Delay

scholarly journals Persistence and Stability for a Class of Forced Positive Nonlinear Delay-Differential Systems

2021 ◽  
Vol 174 (1) ◽  
Author(s):  
D. Franco ◽  
C. Guiver ◽  
H. Logemann
Keyword(s):  
Steady State ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Breeding Programmes ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Nonlinear Delay ◽  
Stability Concept

AbstractPersistence and stability properties are considered for a class of forced positive nonlinear delay-differential systems which arise in mathematical ecology and other applied contexts. The inclusion of forcing incorporates the effects of control actions (such as harvesting or breeding programmes in an ecological setting), disturbances induced by seasonal or environmental variation, or migration. We provide necessary and sufficient conditions under which the states of these models are semi-globally persistent, uniformly with respect to the initial conditions and forcing terms. Under mild assumptions, the model under consideration naturally admits two steady states (equilibria) when unforced: the origin and a unique non-zero steady state. We present sufficient conditions for the non-zero steady state to be stable in a sense which is reminiscent of input-to-state stability, a stability notion for forced systems developed in control theory. In the absence of forcing, our input-to-sate stability concept is identical to semi-global exponential stability.

Sign in / Sign up

Export Citation Format

Share Document