Stability Loss Delay in Harvesting Competing Populations

Abstract

When populations are in competition, it often happens that one of them disappears. Harvesting may be used for the control and management of competing species to stabilize the populations at a persistent equilibrium. A three-dimensional model, where the harvesting effort is a dynamic variable, is studied in the case where the growth rate of the harvesting effort is very slow. The analysis shows that the system can have relaxation oscillations. Dynamic bifurcation theory is used to determine the maximal and minimal values of harvesting effort along this cycle of oscillations. Academic Press

Stability and Bifurcation Analysis for a Two-Competitor/One-Prey System With Two Delays

“…Delayed models similar to (1.2) have been studied widely by many authors and some interesting results have also been obtained (see [1,15,9]). For example, Boudjellaba and Sari [1] investigated the loss of stability by the increase of delay in a three-dimensional competition model. Patra, Maiti and Samanta [15] considered the boundedness and stability in a delayed food chain model with Michaelis-Menten type ratio-dependent functional responses.…”

Stability and bifurcation analysis on a three-species food chain system with two delays

“…Delayed models similar to (1.2) has been investigated widely by many authors and some interesting results have also been obtained, see [17][18][19]. For example, Boudjellaba and Sari in [17] investigated the stability loss arisen from delay in a three-dimensional competition model. Patra, Maiti and Samanta in [18] considered the boundedness and stability criteria in a delayed food chain model with Michaelis-Menten type ratio-dependent functional responses.…”

Almost periodic solutions of a nonlinear ecological model

“…To tackle this problem, feedback control variables can be introduced to the system. For example, Clark [51] and Boudjellaba [52] have recommended harvesting for the control and management of competing species, and the harvesting effort is introduced as a dynamic variable.…”