Three-Dimensional Autonomous Systems and Chaos

Stephen Lynch
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Stephen Lynch: Manchester Metropolitan University

Chapter Chapter 8 in Dynamical Systems with Applications using Python, 2018, pp 185-214 from Springer

Abstract: Abstract Three-dimensional autonomous systems of differential equations are considered. Critical points and stability are discussed and the concept of chaos is introduced. Examples include the Lorenz equations, used as a simple meteorological model and in the theory of lasers; Chua’s circuit, used in nonlinear electronics and radiophysics; and the Belousov-Zhabotinski reaction, used in chemistry and biophysics. All of these systems can display highly complex behavior that can be interpreted from phase portrait analysis or Poincaré maps (see Chapter 9 ).

Keywords: Three-dimensional Autonomous System; BZ Reaction; Plot Phase Portraits; Lorenz Attractor; Import Numpy (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/978-3-319-78145-7_8

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