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Large r

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Part of the Applied Mathematical Sciences book series (AMS,volume 41)

Abstract

Numerical experiments indicate that for σ = 10, b = 8/3 and r > 313, there is a stable symmetric xy periodic orbit. Furthermore, we suggested in Chapter 5 that this periodic orbit and the three stationary points would, for large enough r, make up the whole of the non-wandering set. In this chapter, we show that there are theoretical reasons to expect both of these results. At the same time, we show that qualitatively more complicated large r behaviour may be expected for some values of the parameters σ and b.

Keywords

  • Periodic Orbit
  • Stationary Point
  • Hopf Bifurcation
  • Average Equation
  • Stable Manifold

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  • DOI: 10.1007/978-1-4612-5767-7_7
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© 1982 Springer-Verlag New York Inc.

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Sparrow, C. (1982). Large r. In: The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors. Applied Mathematical Sciences, vol 41. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5767-7_7

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  • DOI: https://doi.org/10.1007/978-1-4612-5767-7_7

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-90775-8

  • Online ISBN: 978-1-4612-5767-7

  • eBook Packages: Springer Book Archive