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- W3008609097 abstract "Ordinary Differential Equation (ODE) models are ubiquitous throughout the sciences, and form the backbone of the branch of mathematics known as applied dynamical systems. However, despite their utility and their analytical and computational tractability, modelers must make certain simplifying assumptions when modeling a system using ODEs. Relaxing (or otherwise changing) these assumptions may lead to the derivation of new ODE or non-ODE models and sometimes these new models can yield results that differ meaningfully in the context of a given application. The goal of this chapter is to explore some approaches to relaxing these ODE model assumptions to derive models which can then be analyzed in ways that parallel or build upon an existing ODE model analysis. To accomplish this, the first part of this chapter (Sect. 2) reviews some common methods for the application and analysis of ODE models. The next section (Sect. 3) explores various ways of deriving new models by modifying the assumptions of existing ODE models. This allows investigators to explore the extent to which ODE model results are robust to changes in model assumptions, and to answer questions that are better addressed using non-ODE models. The last part of this chapter suggests a few specific project ideas (Sect. 4) and encourages undergraduate researchers to share their results through presentations and publications (Sect. 5)." @default.
- W3008609097 created "2020-03-06" @default.
- W3008609097 creator A5083581399 @default.
- W3008609097 date "2020-01-01" @default.
- W3008609097 modified "2023-09-26" @default.
- W3008609097 title "Building New Models: Rethinking and Revising ODE Model Assumptions" @default.
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