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Limit Cycles

In: Nonlinear Physics with Mathematica for Scientists and Engineers

Author

Listed:
  • Richard H. Enns

    (Simon Fraser University, Department of Physics)

  • George C. McGuire

    (University College of the Fraser Valley, Department of Physics)

Abstract

For autonomous nonlinear and non-conservative systems described by the differential equations 7.1 $$\begin{array}{*{20}{c}} {\frac{{dx}}{{dt}} = P(x,y),} & {\frac{{dy}}{{dt}} = Q(x,y)} \\ \end{array}$$ a new kind of trajectory, the limit cycle, has been briefly encountered at various points in the preceding chapters. The Van der Pol (VdP) electronic oscillator with P(x, y) = y and Q(x, y) = ∈(1-x 2)y - x, for example, made its debut in Chapter 2. In this chapter we would like to explore some of the more important properties of limit cycles in greater depth.

Suggested Citation

  • Richard H. Enns & George C. McGuire, 2004. "Limit Cycles," Springer Books, in: Nonlinear Physics with Mathematica for Scientists and Engineers, chapter 0, pages 265-292, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0211-0_7
    DOI: 10.1007/978-1-4612-0211-0_7
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