Weak chaos

A modified form of the logistic equation, Xn + 1 = AXn(1 − sXnp) was examined for the range over which the parameters s and p could be varied without affecting its chaotic behaviour. It was found that the values of s as low as 10−10 had no effect on the magnitude of the Lyapunov exponent but the maximum value of Xn varied as . Changing the magnitude of p in the range 10−10 p 100 had very little effect on the shape or magnitude of the Lyapunov exponent. Some implications of these results are discussed.