Abstract
The Lotka-Volterra system is a classic model of predator–prey interactions, capturing the interdependent growth and decline of two species. Using a dynamical systems approach, we identify fixed points, linearize the system via the Jacobian, and analyze phase space trajectories to determine stability and long-term behavior. This analysis provides insight into predator-prey dynamics without requiring explicit solutions. We further extend the model by incorporating a carrying capacity for the prey, reflecting more realistic population dynamics.
Recommended Citation
Maylath, Amanda and Brensinger, Samuel
(2026)
"Predator-Prey Dynamics: Exploration and Logistic Extension of the Lotka-Volterra System,"
Electronic Proceedings of Undergraduate Mathematics Day: Vol. 9, Article 3.
Available at:
https://ecommons.udayton.edu/epumd/vol9/iss1/3