Can't plot henon map with certain initial conditions (code works for other conditions),

I've created a function to plot Henon map, it works when a=1.4, b=0.3, x0=0, y0=0 and n=10,000. But it doesnt work when a=1.7, b=0.5, x0=0.1, y0=0.1 and n=10,000. I checked the workspace to see the results of x, y and I found that for the the second condition, both x and y becomes -Inf after about only 20 iterations. Can anybody help me with this issue? Lots of thanks!

Below is the code:

function [ x, y ] = Henon( a, b, x0, y0, n )

format long e;

x = zeros( n, 1 );

x(1) = x0;

y = zeros( n, 1 );

y(1) = y0;

for i = 1 : n-1

x(i+1) = 1 + y(i) - a*(x(i)^2);

y(i+1) = b*x(i);

end

figure(2)

plot( x, y );

xlabel( 'x' );

ylabel( 'y' );

title( ['Henon Map (iterations=' num2str(n) ')']);

end

Answer 1

[Subhadeep Koley]

I assume that you are referring to this [1] paper for creating Henon Map. The paper says, for a < 0.122500 or a > 1.55 for b = 0.3, the points always escape to infinity: apparently there exists no attractor in those cases [1]. Only for

0.122500 < a <1.55 depending on the initial values (x0, y0) either the points escape to infinity or they converge towards an attractor. Therefore, the authors adopted a = 1.4, b = 0.3 experimentally.

I think this is the reason why x and y shoots down to -Inf for a = 1.7, b = 0.5.

[1] Hénon, M. A two-dimensional mapping with a strange attractor. Comm. Math. Phys. 50 (1976), no. 1, 69--77.