Stability of the delay logistic equation of population dynamics

2004 ◽  
Author(s):  
M.Yu. Vagina
Keyword(s):  
Population Dynamics ◽  
Logistic Equation ◽  
Delay Logistic Equation

An application of the logistic equation to the population dynamics of salt-marsh gastropods

1974 ◽  
Vol 5 (3) ◽  
pp. 450-459 ◽  
Author(s):  
Garrell E. Long ◽  
Phillip H. Duran ◽  
Ralph O. Jeffords ◽  
Douglas N. Weldon
Keyword(s):  
Population Dynamics ◽  
Salt Marsh ◽  
Logistic Equation

ON THE MODIFIED LOGISTIC EQUATION

2007 ◽  
Vol 17 (08) ◽  
pp. 2541-2546 ◽  
Author(s):  
T. BAKRI
Keyword(s):  
Exact Solution ◽  
Population Dynamics ◽  
Periodic Solution ◽  
Explicit Expression ◽  
Slow Manifold ◽  
Logistic Equation ◽  
Fast System ◽  
Sharp Estimates ◽  
Lift Off

A simple slow-fast system based on the logistic equation for which the exact solution is known, is considered here. We are especially interested in the lift-off point i.e. the point where the solution suddenly leaves the unstable slow manifold after being exponentially close to it for quite some time. Sharp estimates of this point are given. Also a slightly modified system is considered which has a periodic solution of canard type. The explicit expression of this periodic solution is given as well as estimates of its lift-off point. This type of equation can be valuable in modeling population dynamics. Lift-off points can then be used to predict outbreaks of epidemics, which nowadays is an important item in our society.

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