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One Switch in the Plane: A Primer

  • Mike R. Jeffrey
Chapter

Abstract

This chapter presents a short course on dynamical systems with two variables and one switch,
$$\displaystyle{(\dot{x}_{1},\dot{x}_{2}) = \left (f(x_{1},x_{2};\lambda ),\;f(x_{1},x_{2};\lambda )\right )\;,\qquad \lambda =\mathop{ \mathrm{sign}}\nolimits (\sigma (x_{1},x_{2}))\;.}$$
These represent the simplest case of the problems we cover more generally in the rest of the book.

They are the most studied and most easily understood piecewise-smooth problems, in comparison with systems on the real line which are trivial, and higher-dimensional systems which are orders more challenging. Filippov in particular covered planar systems in great detail in [71], so it is a good place to begin summarizing the state of the art and setting off in search of something more.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Mike R. Jeffrey
    • 1
  1. 1.Department of Engineering MathematicsUniversity of BristolBristolUK

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