Global stability for a general population model with time delays

1998 ◽  
pp. 447-457
Author(s):  
Joseph So ◽  
J. Yu
Keyword(s):  
General Population ◽  
Global Stability ◽  
Population Model ◽  
Time Delays

GLOBAL STABILITY OF A NONLINEAR DISCRETE POPULATION MODEL WITH TIME DELAYS

2007 ◽  
Vol 10 (03) ◽  
pp. 315-333
Author(s):  
NA FANG ◽  
XIAOXING CHEN
Keyword(s):  
Global Stability ◽  
Positive Solution ◽  
Positive Solutions ◽  
Population Model ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Volterra Type ◽  
Discrete Population ◽  
Liapunov Functionals ◽  
Discrete Population Model

The global stability of a nonlinear discrete population model of Volterra type is studied. The model incorporates time delays. By linearization of the model at positive solutions and construction of Liapunov functionals, sufficient conditions are obtained to ensure that a positive solution of the model is stable and attracts all positive solutions. An example shows the feasibility of our main results.

Travelling fronts in a food-limited population model with time delay

2002 ◽  
Vol 132 (1) ◽  
pp. 75-89 ◽  
Author(s):  
S. A. Gourley ◽  
M. A. J. Chaplain
Keyword(s):  
Population Model ◽  
Time Delays ◽  
Front Solutions ◽  
Heteroclinic Connection ◽  
Non Local ◽  
Spatial Terms ◽  
Travelling Fronts ◽  
Manifold Theory ◽  
And Diffusion ◽  
Existence Question

In this paper we study travelling front solutions of a certain food-limited population model incorporating time-delays and diffusion. Special attention is paid to the modelling of the time delays to incorporate associated non-local spatial terms which account for the drift of individuals to their present position from their possible positions at previous times. For a particular class of delay kernels, existence of travelling front solutions connecting the two spatially uniform steady states is established for sufficiently small delays. The approach is to reformulate the problem as an existence question for a heteroclinic connection in R4. The problem is then tackled using dynamical systems techniques, in particular, Fenichel's invariant manifold theory. For larger delays, numerical simulations reveal changes in the front's profile which develops a prominent hump.

scholarly journals Permanence of dispersal population model with time delays

2006 ◽  
Vol 192 (2) ◽  
pp. 417-430 ◽  
Author(s):  
Yasuhiro Takeuchi ◽  
Jing’an Cui ◽  
Rinko Miyazaki ◽  
Yasuhisa Saito
Keyword(s):  
Population Model ◽  
Time Delays

PERMANENCE AND GLOBAL STABILITY IN AN IMPULSIVE LOTKA–VOLTERRA N-SPECIES COMPETITIVE SYSTEM WITH BOTH DISCRETE DELAYS AND CONTINUOUS DELAYS

2008 ◽  
Vol 01 (02) ◽  
pp. 179-196 ◽  
Author(s):  
XINZHU MENG ◽  
LANSUN CHEN
Keyword(s):  
Global Stability ◽  
Time Delays ◽  
Asymptotical Stability ◽  
Volterra System ◽  
Competitive System ◽  
Globally Asymptotical Stability ◽  
Discrete Delays ◽  
Impulsive Delay ◽  
Impulsive Perturbations

In this paper, we formulate a robust impulsive Lotka–Volterra n-species competitive system with both discrete delays and continuous delays. Our results in this paper indicate that under the appropriate linear bounded impulsive perturbations, the impulsive delay Lotka–Volterra system remains the original permanence and globally asymptotical stability of the nonimpulsive delay Lotka–Volterra system. We show that the conditions for the permanence and globally asymptotical stability of the system depend on time delays, so, we call it "profitless".

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