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Three-Dimensional Autonomous Systems and Chaos

In: Dynamical Systems with Applications Using MATLAB®

Author

Listed:
  • Stephen Lynch

    (Loughborough University, Department of Computer Science)

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–Zhabotinsky 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 Chap. 17 ).

Suggested Citation

  • Stephen Lynch, 2025. "Three-Dimensional Autonomous Systems and Chaos," Springer Books, in: Dynamical Systems with Applications Using MATLAB®, edition 0, chapter 0, pages 321-347, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-89067-3_16
    DOI: 10.1007/978-3-031-89067-3_16
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