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Predator-prey models with delay and prey harvesting.

A Martin¹, S Ruan

¹Department of Mathematics, University of New Orleans, LA 70148-2900, USA.

Journal of Mathematical Biology

|October 30, 2001

Summary

Time delays can destabilize predator-prey models, but harvesting can stabilize them. Increasing harvesting can restore stability lost due to time delays in ecological models.

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Area of Science:

Mathematical Biology
Ecology
Dynamical Systems

Background:

Predator-prey models exhibit complex dynamics with constant harvesting.
Time delays in ecological models can lead to instability and bifurcations.

Purpose of the Study:

Investigate the combined effects of harvesting rate and time delay.
Analyze dynamics in generalized Gause-type and Wangersky-Cunningham predator-prey models.

Main Methods:

Mathematical modeling of predator-prey systems.
Analysis of equilibrium stability under varying parameters.
Computer simulations to validate theoretical findings.

Main Results:

Time delays can destabilize stable equilibria and cause stability switching.
Harvesting rate stabilizes equilibria below a critical level.
One model lost and then regained stability with increased harvesting.

Conclusions:

Combined effects of time delay and harvesting are crucial for model stability.
Harvesting can counteract destabilizing effects of time delays.
Mathematical and computational approaches reveal complex ecological dynamics.

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