# Issue with Bifurcation Plot for Driven Pendulum

I'm trying to create a bifurcation plot for a driven damped pendulum. In particular, I'm trying to recreate the plot found in Taylor's 'Classical Mechanics' (page 484) for a driving strength $$\gamma$$ in the range $$1.060 \leq \gamma \leq 1.087$$:

I believe I have the code down and I can reproduce the main properties of the plot, however for $$\gamma \geq 1.081$$ the points shift down a couple of units which causes a large discontinuity. I'd appreciate any help on the matter. I've attached an image of my result below.

• I guess you mean the discontinuity around 1.081? – Stéphane Rollandin Apr 10 '18 at 18:29
• Yes, apologies for that. I've looked at the points at that $\gamma$ and compared it to values for the previous value $\gamma-0.001$ and the results do not align. I've ran the algorithm a couple times and each time the same gap appears. Looks unlikely to be a visual bug. – Damian Anslik Apr 10 '18 at 18:32
• Maybe this can help: mathematica.stackexchange.com/q/141653 – Stéphane Rollandin Apr 10 '18 at 18:47
• – Stéphane Rollandin Apr 10 '18 at 18:49
• It might be better to include the equation you're using and perhaps some pseudocode to outline what you're doing. – Kyle Kanos Apr 15 '18 at 12:21

• As the maximum amplitude increases, some numerical angle normalization makes a jump with no meaning (e.g., from $$2\pi$$ to $$4\pi$$) - that might very well be the case here, if "End Position" in your plot is normalized by $$2\pi$$.
• This system exhibits multistability (i.e., it can have more than one stable final state, for a given set of parameter values) and which state is reached depends on which basin of attraction the initial condition belongs to. As $$\gamma$$ is varied, the boundary between different basins moves in phase space, and the fixed initial condition being used to construct the bifurcation diagram might suddenly find itself on a different basin at a certain $$\gamma^*$$: in this way, the diagram shows the bifurcations of attractor $$A$$ for $$\gamma<\gamma^*$$, and of attractor $$B$$ afterwards.