Is this project an undergraduate, graduate, or faculty project?
Undergraduate
Project Type
individual
Campus
Daytona Beach
Authors' Class Standing
Mihil Dimpal Patel,
Lead Presenter's Name
Mihil Dimpal Patel
Lead Presenter's College
DB College of Engineering
Faculty Mentor Name
Dr. Jorge Gonzalez
Abstract
Population growth models are essential tools for understanding how biological populations change over time under environmental constraints. This study examines population dynamics by comparing the classical exponential growth model with the logistic growth model. While exponential growth assumes unlimited resources and results in unbounded population increase, the logistic model incorporates a carrying capacity that limits growth as resources become scarce. To better represent real-world conditions, the logistic model is extended by introducing modifications such as harvesting terms and time-varying carrying capacities, which account for external removal of individuals and changing environmental limits. The equilibria of these models are determined, and their stability is analyzed to understand long-term population behavior. The results illustrate how additional factors such as harvesting pressure and environmental variability influence equilibrium points and can lead to stable populations, population decline, or extinction scenarios. These findings highlight the importance of modified logistic models for accurately describing population dynamics in ecological and resource management contexts.
Did this research project receive funding support (Spark, SURF, Research Abroad, Student Internal Grants, Collaborative, Climbing, or Ignite Grants) from the Office of Undergraduate Research?
No
Included in
Dynamic Systems Commons, Ordinary Differential Equations and Applied Dynamics Commons, Population Biology Commons
Modeling Population Growth with Logistic and Modified Logistic Equations
Population growth models are essential tools for understanding how biological populations change over time under environmental constraints. This study examines population dynamics by comparing the classical exponential growth model with the logistic growth model. While exponential growth assumes unlimited resources and results in unbounded population increase, the logistic model incorporates a carrying capacity that limits growth as resources become scarce. To better represent real-world conditions, the logistic model is extended by introducing modifications such as harvesting terms and time-varying carrying capacities, which account for external removal of individuals and changing environmental limits. The equilibria of these models are determined, and their stability is analyzed to understand long-term population behavior. The results illustrate how additional factors such as harvesting pressure and environmental variability influence equilibrium points and can lead to stable populations, population decline, or extinction scenarios. These findings highlight the importance of modified logistic models for accurately describing population dynamics in ecological and resource management contexts.