this is for holding javascript data
Benedict Irwin edited main.tex
over 9 years ago
Commit id: c8f150d7a31084fa83353a197e25b7bcb8edf28f
deletions | additions
diff --git a/main.tex b/main.tex
index e3060eb..cc87eb3 100644
--- a/main.tex
+++ b/main.tex
...
\end{equation}
Provided the first iteration does not equal zero, the scheme can be coded nicely.
Then one may vary $\alpha$ and $\beta$. Due to initial reasons $\beta$ was set to $0.5$, and $\alpha$ varied from $1$ till $4$, at low values of $\alpha$ the integral converges nicely, at values less than $3$ there is a point where the scheme hops between two
converant convergent values. Luckily, it was noticed at $3.5$ four convergent values appeared, and from prior knowledge (a guess at Lyapunov/Feigenbaum behaviour) I took a sweep for suspected bifurcations. Amazingly, the solution to $I_\alpha(\beta)$ for any $\alpha$ is the logistic map! The tradiditional bifurcation diagram when taking the iteration \begin{equation}
x_{n+1}=rx_n(1+x_n)