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Bifurcations, Equilibria, and Phase Lines: Modern Topics in Differential Equations Courses

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Visit this site: http://math.bu.edu/DYSYS/ode-bif/ode-bif.html
Author:Robert L. Devaney; Dept. of Mathematics, Boston University
Description: Elementary bifurcation theory is topic is rarely included in traditional differential equations courses, yet it is of crucial importance in many engineering applications. In the Boston University Differential Equations project (a joint effort with Paul Blanchard and G. R. Hall), bifurcations form one strand which continually reappears throughout the course. Bifurcations initially arise in the study of first order autonomous equations. They appear again when the qualitative theory of linear systems is discussed. And they show up later in the course when nonlinear systems and discrete dynamical systems are treated. Web pages include: Qualitative approach to autonomous equations; The phase line and the graph of the vector field; Classification of equilibrium points; Bifurcations; An application: harvesting.
Levels: College, Research
Languages: English
Resource Types: Courses
Math Topics: Differential Equations

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