Date of Graduation

Spring 2012

Degree

Master of Natural and Applied Science in Mathematics

Department

Mathematics

Committee Chair

Jorge Rebaza

Keywords

predator-prey models, threshold harvesting, dynamical systems, phase portraits, periodic solutions, bifurcations

Subject Categories

Mathematics

Abstract

The dynamics of two predator-prey models with differing types of prey refuge and the same threshold harvesting policy are studied. Local and global stability properties of the equilibria are analyzed, with emphasis placed on the coexistence of species. How harvesting and refuge affect the dynamics of the systems is analyzed. Sufficient conditions for the existence and non-existence of periodic solutions for each system are established. The existence of several bifurcations for each system is also established analytically and numerically.

Copyright

© Justin Scott Ricklefs

Campus Only

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