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

2002 ◽  
Vol 132 (01) ◽  
pp. 75
Keyword(s):  
Time Delay ◽  
Population Model ◽  
Travelling Fronts

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.

Stability and Neimark—Sacker bifurcation analysis of a food-limited population model with a time delay

2013 ◽  
Vol 22 (3) ◽  
pp. 030204 ◽  
Author(s):  
Xiao-Wei Jiang ◽  
Zhi-Hong Guan ◽  
Xian-He Zhang ◽  
Ding-Xue Zhang ◽  
Feng Liu
Keyword(s):  
Time Delay ◽  
Bifurcation Analysis ◽  
Population Model

POPULATION CYCLES OF THE DOUGLAS-FIR TUSSOCK MOTH (LEPIDOPTERA: LYMANTRIIDAE): THE TIME-DELAY HYPOTHESIS

1978 ◽  
Vol 110 (5) ◽  
pp. 513-518 ◽  
Author(s):  
Alan A. Berryman
Keyword(s):  
Time Delay ◽  
Negative Feedback ◽  
Population Model ◽  
Time Delays ◽  
Population Cycles ◽  
Douglas Fir ◽  
Limited Data ◽  
Moth Population ◽  
Density Dependent ◽  
Tussock Moth

AbstractA simple population model is used to test the hypothesis that Douglas-fir tussock moth population cycles are caused by time-delays in the responses of density-dependent (negative feedback) processes. The limited data that are available do not seriously conflict with this hypothesis.

scholarly journals On oscillation of a food-limited population model with time delay

2003 ◽  
Vol 2003 (1) ◽  
pp. 55-66 ◽  
Author(s):  
Leonid Berezansky ◽  
Elena Braverman
Keyword(s):  
Differential Equation ◽  
Time Delay ◽  
Delay Differential Equation ◽  
Population Model ◽  
Delay Differential ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay ◽  
Oscillation And Nonoscillation

For a scalar nonlinear delay differential equationṄ(t) = r(t)N(t)(K − N(h(t)))/(K + s(t)N(g(t))),r(t) ≥ 0, h(t) ≤ t, g(t) ≤ tand some generalizations of this equation, we establish explicit oscillation and nonoscillation conditions. Coefficientr(t)and delays are not assumed to be continuous.

Dynamics of a Scalar Population Model with Delayed Allee Effect

2018 ◽  
Vol 28 (12) ◽  
pp. 1850153
Author(s):  
Xiaoyuan Chang ◽  
Junping Shi ◽  
Jimin Zhang
Keyword(s):  
Time Delay ◽  
Population Model ◽  
Allee Effect ◽  
Single Point ◽  
Basin Of Attraction ◽  
Basins Of Attraction ◽  
Global Extinction ◽  
Stable Equilibria ◽  
The Stability ◽  
Parameter Values

A scalar population model with delayed growth rate of Allee effect type is considered in this paper. The stability of equilibria and associated supercritical Hopf bifurcations are analyzed. The basins of attraction of the two locally stable equilibria are characterized in terms of parameter values. In particular, when the time delay is large, the basin of attraction of the persistence equilibrium and limit cycle shrinks to a single point, so a global extinction of population occurs as a combined result of Allee effect and time delay.

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