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Full-Text Articles in Life Sciences
1-65-S-Algal Blooms: Algal Blooms Threatening Lake Chapala, R. Corban Harwood
1-65-S-Algal Blooms: Algal Blooms Threatening Lake Chapala, R. Corban Harwood
Faculty Publications - Department of Mathematics
This modeling scenario investigates the massive algal blooms that struck Lake Chapala, Mexico, starting in 1994. After reading a summary of articles written on the incidents, students are guided through the process of creating a first order differential equation from a verbal model of the factors and analyze the nonautonomous ODE using direction field, parameter evaluation, and exact solution computation to fully describe the population behavior. Students are expected to be familiar with the separable method and direction fields. Students will learn building and improving a model from qualitative descriptions, nondimensionalization, evaluating parameters, and how to use DFIELD software to …
Algae Population Self-Replenishment, R. Corban Harwood
Algae Population Self-Replenishment, R. Corban Harwood
Faculty Publications - Department of Mathematics
This modeling scenario investigates the massive algal blooms that struck Lake Chapala, Mexico, in 1994. After reading a summary of news articles on the incident, students create an ODE system model from a verbal description of the factors, visualize this system using an executable Java applet (PPLANE) to predict overall behavior, and then analyze the nonlinear system using the Jacobian matrix, eigenvalues, phase plane, and feasibility conditions on parameters to fully describe the system behavior. Students are expected to be familiar with systems of differential equations, equilibria, jacobian matrices, and eigenvalues. Students will learn modeling from qualitative descriptions, nondimensionalization, applying …
Modeling Algae Self-Replenishment, V. S. Manoranjan, Miguel A. Olmos Gomez, R. Corban Harwood
Modeling Algae Self-Replenishment, V. S. Manoranjan, Miguel A. Olmos Gomez, R. Corban Harwood
Faculty Publications - Department of Mathematics
This paper presents a sunlight-dependent algae growth model. Driven by the circumstances surrounding Lake Chapala, Mexico, this theoretical model is an endeavor to understand the resilient sustainability of algae that threatens the area’s ecosystem. In this paper, free-floating algae (phytoplankton) are treated as two distinct populations according to their location in the body of water: the vibrant sunlit upper region and the stagnate lower region where photosynthesis is not possible. The numerical solution for the model is analyzed and results are discussed in light of previous studies and the state of Lake Chapala.