Instructions: To zoom in on an area, highlight it with mouse by dragging out a rectangle. Reset button will set default parameters.
Description:
Bifurcatoin first appears during study of logistic equation:
xn+1 = xn + r*xn*(1 - xn)
This equation was used to model population growth. xn+1 is a new population, xn is an old population and r is rate of growth. For r < 2.0 the solution is usually stable. This equation was derrived by Pierre François Verhulst (1804-1849). Later in 70's Mitchel Feigenbaum studied lots of bifurcations. He found that ratios of lengths of adjacent areas of bifuraction is constant and equal to Feignebaum number.
You can use following eqations:
Bifurcation:
xn+1 = r*f(xn)*(1 - f(xn))
Verhulst:
xn+1 = xn + r*f(xn)*(1 - f(xn))
Feigenbaum:
xn+1 = xn + r*sin(PI*xn)
Feigenbaum 2:
xn+1 = r*sin(PI*xn)
Stewart map:
xn+1 = r*f(xn)*f(xn) - 1
May map:
xn+1 = r*xn/((1+xn)^b)
where f is a function: abs, arccos, arcsin, arctan, cos, cosh, exp. log, sin, sinh, sqrt, tan, tanh. none means that is used default function. Cycles is the cycles number that is made before poits are plotted. They are used to stablize solution. MaxIter is number of points that are plotted.