Analysis of a Model Representing Stage-Structured Population Growth with State-Dependent Time Delay

1992 ◽  
Vol 52 (3) ◽  
pp. 855-869 ◽  
Author(s):  
Walter G. Aiello ◽  
H. I. Freedman ◽  
J. Wu
Keyword(s):  
Time Delay ◽  
Population Growth ◽  
Structured Population ◽  
State Dependent

Harvesting on a State-Dependent Time Delay Model

2020 ◽  
Vol 8 (1) ◽  
pp. 82-96
Author(s):  
Ruijun Xie ◽  
Xin Zhang ◽  
Wei Zhang
Keyword(s):  
Time Delay ◽  
Population Density ◽  
Positive Equilibrium ◽  
Delay Model ◽  
Stability Criteria ◽  
State Dependent ◽  
State Dependent Delay ◽  
Cooperation Model ◽  
Increasing Function ◽  
Positivity And Boundedness

AbstractIn this paper, we propose and analyze a cooperation model with harvesting and state-dependent delay, which is assumed to be an increasing function of the population density with lower and upper bound. The main purpose of this article is to obtain the dynamics of our model analytically by controlling the harvesting. We present results on positivity and boundedness of all populations. Criteria for the existence of all equilibria and uniqueness of a positive equilibrium are given by controlling the harvesting. Finally, the global exponentially asymptotical stability criteria of model is obtained by the improved Hanalay inequality.

Bifurcation and stability of periodic solutions of differential equations with state-dependent delays

2003 ◽  
Vol 14 (1) ◽  
pp. 3-14 ◽  
Author(s):  
D. SCHLEY
Keyword(s):  
Time Delay ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Perturbation Methods ◽  
Population Models ◽  
Delay Function ◽  
State Dependent ◽  
The Stability ◽  
Bifurcation And Stability

We consider periodic solutions which bifurcate from equilibria in simple population models which incorporate a state-dependent time delay of the discrete kind. The delay is a function of the current size of the population. Solutions near equilibria are constructed using perturbation methods to determine the sub/supercriticality of the bifurcation and hence their stability. The stability of the bifurcating solutions depends on the qualitative form of the delay function. This is in contrast to the stability of an equilibrium, which is determined purely by the actual value of this function at the equilibrium.

scholarly journals STATE-DEPENDENT DELAYS ASSOCIATED TO THRESHOLD PHENOMENA IN STRUCTURED POPULATION DYNAMICS

2007 ◽  
Vol 17 (06) ◽  
pp. 877-900 ◽  
Author(s):  
MY LHASSAN HBID ◽  
EVA SÁNCHEZ ◽  
RAFAEL BRAVO DE LA PARRA
Keyword(s):  
Population Dynamics ◽  
Unified Approach ◽  
Structured Population ◽  
Threshold Phenomena ◽  
State Dependent ◽  
Characteristic Lines ◽  
Structured Population Dynamics ◽  
Insect Populations ◽  
The Common ◽  
Age Structured

The aim of this paper is to put in evidence the onset of state-dependent delays in threshold models for structured population dynamics. A unified approach to these models is provided, based on solving the corresponding balance law (hyperbolic P.D.E.) along the characteristic lines and showing the common underlying ideas. Size and age-structured models in different fields are presented: insect populations, cell proliferation and epidemics.

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