Planar Systems

Stephen Lynch
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Stephen Lynch: Manchester Metropolitan University

Chapter Chapter 3 in Dynamical Systems with Applications using Python, 2018, pp 65-94 from Springer

Abstract: Abstract To introduce the theory of planar autonomous linear differential equations. To extend the theory of linear systems to that of nonlinear systems. On completion of this chapter, the reader should be able to find and classify critical points in the plane; carry out simple linear transformations; construct phase plane diagrams using nullclines, vector fields, and eigenvectors; apply the theory to simple modeling problems. Basic analytical methods for solving two-dimensional linear autonomous differential equations are reviewed and simple phase portraits are constructed in the plane.

Date: 2018
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DOI: 10.1007/978-3-319-78145-7_3

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