Robustness and asymptotic stability for the Winfree model on a general network under the effect of time-delay

2018 ◽  
Vol 59 (11) ◽  
pp. 112702
Author(s):  
Seung-Yeal Ha ◽  
Doheon Kim
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Winfree Model ◽  
General Network

Qualitative analysis of a chemostat model with inhibitory exponential substrate uptake and a time delay

2014 ◽  
Vol 07 (04) ◽  
pp. 1450045 ◽  
Author(s):  
Qinglai Dong ◽  
Wanbiao Ma
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Qualitative Analysis ◽  
Numerical Simulations ◽  
Global Asymptotic Stability ◽  
Positive Equilibrium ◽  
Substrate Uptake ◽  
Sufficient Condition ◽  
Chemostat Model ◽  
Local Asymptotic Stability

In this paper, we consider a simple chemostat model with inhibitory exponential substrate uptake and a time delay. A detailed qualitative analysis about existence and boundedness of its solutions and the local asymptotic stability of its equilibria are carried out. Using Lyapunov–LaSalle invariance principle, we show that the washout equilibrium is global asymptotic stability for any time delay. Using the fluctuation lemma, the sufficient condition of the global asymptotic stability of the positive equilibrium [Formula: see text] is obtained. Numerical simulations are also performed to illustrate the results.

Asymptotic stability analysis and model reduction for spatially interconnected time-delay systems

2020 ◽  
Vol 357 (17) ◽  
pp. 12670-12699
Author(s):  
Hui Wang ◽  
Huiling Xu ◽  
Xiaokai Zhai ◽  
Xuefeng Chen ◽  
Zhiping Lin
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Asymptotic Stability ◽  
Model Reduction ◽  
Delay Systems ◽  
Time Delay Systems
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