ORCID

https://orcid.org/0009-0004-1778-0290

Year

2025

Season

Spring

Paper Type

Master's Thesis

College

College of Arts and Sciences

Degree Name

Master of Science in Mathematical Sciences (MS)

Department

Mathematics & Statistics

NACO controlled Corporate Body

University of North Florida. Department of Mathematics and Statistics

Committee Chairperson

Dr. Mohammad M. Rahman

Second Advisor

Dr. Mei-Qin Zhan

Rights Statement

http://rightsstatements.org/vocab/InC/1.0/

Third Advisor

Dr. Kening Wang

Department Chair

Dr. Richard F. Patterson

College Dean

Dr. Kaveri Subrahmanyam

Abstract

This study investigates the dynamics of mutualistic relationships between two prey species in the presence of a predator, by taking into account herding in one species along with the influence of carrying capacities between two prey species. These mutualistic dynamics are presented by constructing two mathematical models, namely an indirect and direct mutualism model. As the strength of the symbiotic relationship increases the indirect model goes through transcritical bifurcation to Hopf bifurcation whereas in the direct mutualism model goes through saddle-node bifurcation to Hopf bifurcation.

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