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Three-Dimensional Autonomous Systems and Chaos

In: Dynamical Systems with Applications using Python

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  • Stephen Lynch

    (Manchester Metropolitan University)

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 ).

Suggested Citation

  • Stephen Lynch, 2018. "Three-Dimensional Autonomous Systems and Chaos," Springer Books, in: Dynamical Systems with Applications using Python, chapter 0, pages 185-214, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-78145-7_8
    DOI: 10.1007/978-3-319-78145-7_8
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