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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