Poincaré Maps and Nonautonomous Systems in the Plane

Stephen Lynch
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Stephen Lynch: Manchester Metropolitan University School of Computing, Mathematics & Digital Technology, Department of Computing and Mathematics

Chapter Chapter 15 in Dynamical Systems with Applications using MATLAB®, 2014, pp 311-334 from Springer

Abstract: Abstract Aims and Objectives • To introduce the theory of Poincaré maps. • To compare periodic and quasiperiodic behavior. • To introduce Hamiltonian systems with two degrees of freedom. • To use Poincaré maps to investigate a nonautonomous system of differential equations. On completion of this chapter the reader should be able to • understand the basic theory of Poincaré maps; • plot return maps for certain systems; • use the Poincaré map as a tool for studying stability and bifurcations.

Keywords: Hamiltonian System; Phase Portrait; Bifurcation Diagram; Unstable Manifold; Nonautonomous System (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-06820-6_15

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DOI: 10.1007/978-3-319-06820-6_15

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