In case of Hennon map two parameters $a$ and $b$ to be set.The Hénon map takes a point $(x_n, y_n)$ in the plane and maps it to a new point $x_{n+1} = 1-a x_n^2 + y_n$, $y_{n+1} = b x_n$. The map depends on two parameters, a and b, which for the classical Hénon map have values of a = 1.4 and b = 0.3. For the classical values the Hénon map is chaotic.
What are other value of $a$ and $b$ for which we would also get chaotic nature? Can anyone suggest interval for $a$ and $b$?
You can check a bifurcation diagram or a graph of maximum Lyapunov exponents to find other values which lead to chaos. Below is the bifurcation diagram for b=0.3 and varying values of a. Chaotic intervals are obvious.