ERIC Number: EJ770372
Record Type: Journal
Publication Date: 2002-Jan
Stability Criteria for Differential Equations with Variable Time Delays
Schley, D.; Shail, R.; Gourley, S. A.
International Journal of Mathematical Education in Science and Technology, v33 n3 p359-375 Jan 2002
Time delays are an important aspect of mathematical modelling, but often result in highly complicated equations which are difficult to treat analytically. In this paper it is shown how careful application of certain undergraduate tools such as the Method of Steps and the Principle of the Argument can yield significant results. Certain delay differential equations arising in population dynamics may serve as good teaching examples for these methods. The determination of linear stability properties for an ordinary differential equation with a varying time delay is carried out through discrete point analysis, either by seeking explicit solutions or leading to the consideration of a difference equation and the roots of a characteristic polynomial. Numerical simulations carried out using MATLAB Simulink are compared to the analytical solutions, and computation is also used to suggest extensions to some results.
Descriptors: Teaching Methods, Equations (Mathematics), Calculus, Mathematical Models, Undergraduate Students, Mathematical Concepts, Technology Uses in Education, Simulation, Computation
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Authoring Institution: N/A